The authors investigated cost models that incorporate quality, access, and efficiency to provide ... more The authors investigated cost models that incorporate quality, access, and efficiency to provide decision support for resource forecasting in the multi-billion-dollar U.S. Army health system. As the Army relocates thousands of troops, the medical system must plan for changes in demand; this study supports that effort. Loglinear cost models that include data envelopment analysis (DEA) efficiency scores were evaluated through ordinary least squares estimation, ridge regression, and robust regression, and serve as the analytical framework. Parsimonious models that incorporate a simple volume-complexity metric, a DEA metric, a quality metric, and medical center status variable provide superior forecasting capability.
Looking back at the past several years leading to this dissertation I cannot help but wonder if I... more Looking back at the past several years leading to this dissertation I cannot help but wonder if I could have gotten here without all the trust, support, and encouragement of so many people around me. I'm grateful to Sherry, my wife, with whom I've shared the joys and troubles of every day for the last few years, and who has always showed love, happiness, and affection. My mother, father, and brother, Csilla, László, and Gábor Ugray, have supported me in every imaginable way, every day, despite the thousands of miles we had to live apart. There is not enough space here to list all my family and numerous good friends from Austin, from my home country, and from all over the world, who cheered me up with their high spirits and gave me encouragement, motivation, often unknown even to themselves. I'm greatly indebted to my Supervisor, Leon Lasdon, who not only patiently guided me through the process of this research, but who also gave me the opportunity to learn a lot from him, not only academically. Many thanks are due to my committee members, Patrick Jaillet, Gang Yu, and Jonathan Bard for their suggestions and their availability for advice. Special thanks are due to John Plummer, whose resources are limitless when it comes to coding, as proved by the GAMS interface. I'd also like to thank Fred Glover, Manuel Laguna, and Jim Kelly of the University of Colorado, Boulder, for their assistance in letting me use OptQuest, their Scatter Search implementation, as a component of OQGRG. Listening to their experiences helped make the algorithm better. Again, there is not enough room to mention everyone at UT Austin, in the Graduate School of Business and in the MSIS Department, who made my experience here so wonderful, exciting, and intellectually stimulating. They gave me many opportunities for growth as a scholar and as a person. v .
Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with m... more Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint. The variables of this problem are a scaling and phase shill applied to the output of each sensor. This problem is solved by applying Lagrangian relaxation to the convex quadratic constraints. Extensive computational experience shows that this approach can efficiently find near-optimal solutions of problems with up to 391 variables and 579 constraints.
Gasoline blending is a critical refinery operation. In 1980, Texaco began developing an improved,... more Gasoline blending is a critical refinery operation. In 1980, Texaco began developing an improved, optimization based, decision support system for planning and scheduling its blending operations. The system, OMEGA, is implemented on personal computers and on larger computer systems. It relies on refinery data bases and on-line data acquisition and exploits detailed nonlinear models of gasoline attributes. Texaco uses OMEGA in all seven US refineries and its Canadian and Welsh refineries. Its benefits include an estimated $30 million annually, better quality control, improved planning and marketing information, and the ability to conduct a variety of what-if studies.
In teaching nonlinear programming (NLP) to undergraduate and graduate students majoring in engine... more In teaching nonlinear programming (NLP) to undergraduate and graduate students majoring in engineering or operations research, we have changed our instructional objectives, course content, and approaches to teaching because of recent dramatic improvements in optimization software and computer hardware. Our primary instructional innovation is to use cooperative active learning methods rather than a traditional lecture format.
The Journal of Defense Modeling and Simulation, Mar 10, 2010
In this study we describe a stochastic optimization model for the relocation of deployable milita... more In this study we describe a stochastic optimization model for the relocation of deployable military hospitals, the reallocation of hospital beds, and the emplacement of tactical medical evacuation assets (medical evacuation helicopters and ground ambulances) during steady-state military combat operations (stability operations). The network model is built around an intuitive objective function, one that is derived from military doctrine. The objective to be minimized is the time traveled, weighted by patient severity, from the evacuation site to the point of injury and onward to the hospital location. The optimal solution also determines the number of air and ground ambulances and the hospital beds of each type required at each selected site. Since future casualty locations, numbers, and severities are uncertain, this information is treated as a number of casualty scenarios with assigned scenario probabilities. The number, location, and severities of casualties can be randomly generated, or provided as part of a planning process. The model then seeks a single set of hospital and vehicle locations, plus the paths the evacuation assets should take in each scenario, which minimize expected travel time over all scenarios. The scenario generator is based on realistic historical data from Operation Iraqi Freedom. Since mobile hospitals provide the primary surgical treatment intervention while dedicated ground and air evacuation assets provide the transportation along evacuation paths, the study objective is important for military medical planners, especially those involved in tactical medical evacuation and treatment planning.
An interior point algorithm for general nonlinear programs is presented. Inequality constraints a... more An interior point algorithm for general nonlinear programs is presented. Inequality constraints are converted to equalities with slack variables. All bounds are handled with a barrier term in the objective. The Kuhn-Tucker system of the resulting equality constrained barrier problem is solved directly by Newton's Method. Primal-Dual, Primal, and Primal-Dual with trust region variants are developed and evaluated. An implementation which utilizes the true Lagrangian Hessian and exploits Jacobian and Hessian sparsity is described. Computational results are presented and discussed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
International Symposium on Systems Optimization and Analysis, 1979
With the concept of optimization being such a central theme in economic theory, planning economis... more With the concept of optimization being such a central theme in economic theory, planning economists have always been attracted to mathematical programming as it provides a natural framework of analysis for theoretical and applied work. Although, nonlinear optimizing economic planning models have been specified and studied for more than 20 years [4, 17] few were ever solved on a routine basis. This stands in sharp contrast to linear programming models which, due to highly reliable (commercial) software are the workhorses of many planning agencies. Even today, most large-scale nonlinear planning models are solved with specifically designed algorithms, tailored around some high performance LP system [9, 14, 16].
This paper demonstrates the feasibility of applying generalized reduced gradient nonlinear progra... more This paper demonstrates the feasibility of applying generalized reduced gradient nonlinear programming methods to solve optimal control models for petroleum reservoir development planning and management. The objective of the models is to maximize present value of profits, and their decision variables are how many wells to drill in each time period, the production rates, abandonment time, and platform size. The analysis uses tank-type reservoir models to describe the reservoir dynamics, and models both a gas reservoir with water drive, and a three phase oil reservoir. Results of several case studies on each model are presented. Extensions that consider spatial variation in the reservoir and use grid reservoir models are being investigated.
This paper describes a methodology for investigating optimal production polices for hydrocarbon r... more This paper describes a methodology for investigating optimal production polices for hydrocarbon reservoirs by an approach that brings together reservoir simulation models and numerical optimization techniques. It describes the results of applying this methodology to a dry gas storage reservoir using a single phase, two-dimensional reservoir simulator. The paper investigates optimal production strategies for several optimization criteria and potential constraints on reservoir operations, and discusses extensions to more complex systems.
Journal of Water Resources Planning and Management, 2004
Water resources planning involves groups or institutions having differing objectives, responsibil... more Water resources planning involves groups or institutions having differing objectives, responsibilities, and interests, and it requires collaboration for conflict resolution. In this paper, the characteristics and modeling requirements of conflict resolution in water resources planning are discussed. A method based on compound models is proposed for regional water resources planning involving multiple decision makers. This method combines modeling techniques such as multiobjective analysis and multicriteria and ...
Gasoline blending is a critical refinery operation. In the 1980s, Texaco developed OMEGA, an opti... more Gasoline blending is a critical refinery operation. In the 1980s, Texaco developed OMEGA, an optimization-based decision support system, to assist in planning and scheduling its blending operations. OMEGA ran primarily on minicomputers and on a mainframe computer system. In 1990, Texaco began replacing OMEGA with StarBlend, a Microsoft Windows application, running on personal computers and client-server networks. StarBlend uses a multi-period extension of OMEGA’s blending model written in the GAMS modeling language and extracts model data from relational databases. Its improved features make it easier to use and it enables blenders and blend planners to more readily incorporate future requirements into current blending decisions. Currently, StarBlend is operational in all Texaco refineries. As federal and state regulations on auto emissions become more complex, StarBlend’s importance will continue to increase.
This paper describes modifications to two multistart algorithms for global optimization which ena... more This paper describes modifications to two multistart algorithms for global optimization which enable them to find feasible solutions to a system of nonlinear constraints more efficiently. The multistart algorithms, called OptQuest-NLP (OQNLP) and Multistart-NLP (MSNLP), start a local NLP Solver from a set of starting points and return the best solution found. Candidate starting points are generated either by a scatter search heuristic or by a randomized process. Two adaptive filters choose a small subset of the candidate points as starting points. The modifications to facilitate feasibility seeking include replacing the exact penalty function used to measure the goodness of a starting point with the sum of infeasibilities, and terminating when a feasible solution is found. We describe experimental results on a large and diverse set of smooth nonlinear nonconvex problems coded in the GAMS modeling language. These are chosen so that a single application of a selected solver from the user-specified starting point terminates infeasible, yet the problems all have feasible solutions. Our results show that MSNLP's feasibility mode is able to find feasible solutions to almost all problems. It is moderately faster than MSNLP not using feasibility mode, and is somewhat better a finding feasible solutions when they exist. It is now an option within MSNLP, and can be invoked by inserting an appropriate record into the options file.
Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objec... more Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objectives and constraints. However, in large and highly nonlinear models, these algorithms can fail to ®nd feasible solutions, or converge to local solutions which are not global. Evolutionary search procedures in general, and genetic algorithms (GAs) speci®cally, are less susceptible to the presence of local solutions. However, they often exhibit slow convergence, especially when there are many variables, and have problems ®nding feasible solutions in constrained problems with``narrow'' feasible regions. In this paper, we describe strategies for solving large nonlinear water resources models management, which combine GAs with linear programming. The key idea is to identify a set of complicating variables in the model which, when ®xed, render the problem linear in the remaining variables. The complicating variables are then varied by a GA. This GA&LP approach is applied to two nonlinear models: a reservoir operation model with nonlinear hydropower generation equations and nonlinear reservoir topologic equations, and a long-term dynamic river basin planning model with a large number of nonlinear relationships. For smaller instances of the reservoir model, the CONOPT2 nonlinear solver is more accurate and faster, but for larger instances, the GA&LP approach ®nds solutions with signi®cantly better objective values. The multiperiod river basin model is much too large to be solved in its entirety. The complicating variables are chosen here so that, when they are ®xed, each period's model is linear, and these models can be solved sequentially. This approach allows sucient model detail to be retained so that long-term sustainability issues can be explored.
IEEE Transactions on Systems Science and Cybernetics, 1968
The problem considered is that of obtaining solutions to large nonlinear mathematical programs by... more The problem considered is that of obtaining solutions to large nonlinear mathematical programs by coordinated solution of smaller subproblems. If all functions in the original problem are additively separable, this can be done by finding a saddle point for the associated Lagrangian function. Coordination is then accomplished by shadow prices, with these prices chosen to solve a dual program. Characteristics of the dual program are investigated, and an algorithm is proposed in which subproblems are solved for given shadow prices. These solutions provide the value and gradient of the dual function, and this information is used to update the shadow prices so that the dual problem is brought closer to solution. Application to two classes of problems is given. The first class is one whose constraints describe a system of coupled subsystems; the second is a class of multi-item inventory problems whose decision variables may be discrete.
Several factors imply an increase in the use of nonlinear optimization models. We face serious pr... more Several factors imply an increase in the use of nonlinear optimization models. We face serious problems of declining productivity and increasingly scarce, expensive raw materials. Computers are becoming cheaper and faster, and more efficient nonlinear programming (NLP) algorithms are being developed. This paper attempts to illustrate the potential of NLP by describing the application of nonlinear programming models to three classes of problems: petrochemical industry applications, nonlinear networks, and economic planning. Problems in the petrochemical industry ranging from product blending, refinery unit optimization, and unit design to multiplant production, and distribution planning are discussed. The nonlinear networks topic includes electric power dispatch, hydroelectric reservoir management, and problems involving traffic flow in urban transportation networks. In economic planning, we describe NLP applications involving large dynamic econometric models, a variety of static equ...
This paper reports on progress in nonlinear programming software since 1979. Developments in the ... more This paper reports on progress in nonlinear programming software since 1979. Developments in the computer industry have had a significant impact on the design of mathematical software and the expectations of users. Microcomputers in particular are changing the software industry to an extent that was not anticipated in the last survey. Continuing refinements in NLP algorithms have enabled users to solve larger and more complicated problems, even some with integer variables. Modeling systems with nonlinear programming capabilities have now become available. Interest and improvements in computational experimentation have increased the rigor and objectivity of studies assessing software quality. This report surveys these important developments and speculates on the future.
IEEE Transactions on Systems, Man, and Cybernetics, 1971
The content of this very interesting book is developed in 26 chapters and one appendix. The scope... more The content of this very interesting book is developed in 26 chapters and one appendix. The scope is very broad: the author advances an exhaustive treatment of the nodal analysis of power systems, as considered and developed for the past two decades by the writer and others ...
The authors investigated cost models that incorporate quality, access, and efficiency to provide ... more The authors investigated cost models that incorporate quality, access, and efficiency to provide decision support for resource forecasting in the multi-billion-dollar U.S. Army health system. As the Army relocates thousands of troops, the medical system must plan for changes in demand; this study supports that effort. Loglinear cost models that include data envelopment analysis (DEA) efficiency scores were evaluated through ordinary least squares estimation, ridge regression, and robust regression, and serve as the analytical framework. Parsimonious models that incorporate a simple volume-complexity metric, a DEA metric, a quality metric, and medical center status variable provide superior forecasting capability.
Looking back at the past several years leading to this dissertation I cannot help but wonder if I... more Looking back at the past several years leading to this dissertation I cannot help but wonder if I could have gotten here without all the trust, support, and encouragement of so many people around me. I'm grateful to Sherry, my wife, with whom I've shared the joys and troubles of every day for the last few years, and who has always showed love, happiness, and affection. My mother, father, and brother, Csilla, László, and Gábor Ugray, have supported me in every imaginable way, every day, despite the thousands of miles we had to live apart. There is not enough space here to list all my family and numerous good friends from Austin, from my home country, and from all over the world, who cheered me up with their high spirits and gave me encouragement, motivation, often unknown even to themselves. I'm greatly indebted to my Supervisor, Leon Lasdon, who not only patiently guided me through the process of this research, but who also gave me the opportunity to learn a lot from him, not only academically. Many thanks are due to my committee members, Patrick Jaillet, Gang Yu, and Jonathan Bard for their suggestions and their availability for advice. Special thanks are due to John Plummer, whose resources are limitless when it comes to coding, as proved by the GAMS interface. I'd also like to thank Fred Glover, Manuel Laguna, and Jim Kelly of the University of Colorado, Boulder, for their assistance in letting me use OptQuest, their Scatter Search implementation, as a component of OQGRG. Listening to their experiences helped make the algorithm better. Again, there is not enough room to mention everyone at UT Austin, in the Graduate School of Business and in the MSIS Department, who made my experience here so wonderful, exciting, and intellectually stimulating. They gave me many opportunities for growth as a scholar and as a person. v .
Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with m... more Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint. The variables of this problem are a scaling and phase shill applied to the output of each sensor. This problem is solved by applying Lagrangian relaxation to the convex quadratic constraints. Extensive computational experience shows that this approach can efficiently find near-optimal solutions of problems with up to 391 variables and 579 constraints.
Gasoline blending is a critical refinery operation. In 1980, Texaco began developing an improved,... more Gasoline blending is a critical refinery operation. In 1980, Texaco began developing an improved, optimization based, decision support system for planning and scheduling its blending operations. The system, OMEGA, is implemented on personal computers and on larger computer systems. It relies on refinery data bases and on-line data acquisition and exploits detailed nonlinear models of gasoline attributes. Texaco uses OMEGA in all seven US refineries and its Canadian and Welsh refineries. Its benefits include an estimated $30 million annually, better quality control, improved planning and marketing information, and the ability to conduct a variety of what-if studies.
In teaching nonlinear programming (NLP) to undergraduate and graduate students majoring in engine... more In teaching nonlinear programming (NLP) to undergraduate and graduate students majoring in engineering or operations research, we have changed our instructional objectives, course content, and approaches to teaching because of recent dramatic improvements in optimization software and computer hardware. Our primary instructional innovation is to use cooperative active learning methods rather than a traditional lecture format.
The Journal of Defense Modeling and Simulation, Mar 10, 2010
In this study we describe a stochastic optimization model for the relocation of deployable milita... more In this study we describe a stochastic optimization model for the relocation of deployable military hospitals, the reallocation of hospital beds, and the emplacement of tactical medical evacuation assets (medical evacuation helicopters and ground ambulances) during steady-state military combat operations (stability operations). The network model is built around an intuitive objective function, one that is derived from military doctrine. The objective to be minimized is the time traveled, weighted by patient severity, from the evacuation site to the point of injury and onward to the hospital location. The optimal solution also determines the number of air and ground ambulances and the hospital beds of each type required at each selected site. Since future casualty locations, numbers, and severities are uncertain, this information is treated as a number of casualty scenarios with assigned scenario probabilities. The number, location, and severities of casualties can be randomly generated, or provided as part of a planning process. The model then seeks a single set of hospital and vehicle locations, plus the paths the evacuation assets should take in each scenario, which minimize expected travel time over all scenarios. The scenario generator is based on realistic historical data from Operation Iraqi Freedom. Since mobile hospitals provide the primary surgical treatment intervention while dedicated ground and air evacuation assets provide the transportation along evacuation paths, the study objective is important for military medical planners, especially those involved in tactical medical evacuation and treatment planning.
An interior point algorithm for general nonlinear programs is presented. Inequality constraints a... more An interior point algorithm for general nonlinear programs is presented. Inequality constraints are converted to equalities with slack variables. All bounds are handled with a barrier term in the objective. The Kuhn-Tucker system of the resulting equality constrained barrier problem is solved directly by Newton's Method. Primal-Dual, Primal, and Primal-Dual with trust region variants are developed and evaluated. An implementation which utilizes the true Lagrangian Hessian and exploits Jacobian and Hessian sparsity is described. Computational results are presented and discussed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
International Symposium on Systems Optimization and Analysis, 1979
With the concept of optimization being such a central theme in economic theory, planning economis... more With the concept of optimization being such a central theme in economic theory, planning economists have always been attracted to mathematical programming as it provides a natural framework of analysis for theoretical and applied work. Although, nonlinear optimizing economic planning models have been specified and studied for more than 20 years [4, 17] few were ever solved on a routine basis. This stands in sharp contrast to linear programming models which, due to highly reliable (commercial) software are the workhorses of many planning agencies. Even today, most large-scale nonlinear planning models are solved with specifically designed algorithms, tailored around some high performance LP system [9, 14, 16].
This paper demonstrates the feasibility of applying generalized reduced gradient nonlinear progra... more This paper demonstrates the feasibility of applying generalized reduced gradient nonlinear programming methods to solve optimal control models for petroleum reservoir development planning and management. The objective of the models is to maximize present value of profits, and their decision variables are how many wells to drill in each time period, the production rates, abandonment time, and platform size. The analysis uses tank-type reservoir models to describe the reservoir dynamics, and models both a gas reservoir with water drive, and a three phase oil reservoir. Results of several case studies on each model are presented. Extensions that consider spatial variation in the reservoir and use grid reservoir models are being investigated.
This paper describes a methodology for investigating optimal production polices for hydrocarbon r... more This paper describes a methodology for investigating optimal production polices for hydrocarbon reservoirs by an approach that brings together reservoir simulation models and numerical optimization techniques. It describes the results of applying this methodology to a dry gas storage reservoir using a single phase, two-dimensional reservoir simulator. The paper investigates optimal production strategies for several optimization criteria and potential constraints on reservoir operations, and discusses extensions to more complex systems.
Journal of Water Resources Planning and Management, 2004
Water resources planning involves groups or institutions having differing objectives, responsibil... more Water resources planning involves groups or institutions having differing objectives, responsibilities, and interests, and it requires collaboration for conflict resolution. In this paper, the characteristics and modeling requirements of conflict resolution in water resources planning are discussed. A method based on compound models is proposed for regional water resources planning involving multiple decision makers. This method combines modeling techniques such as multiobjective analysis and multicriteria and ...
Gasoline blending is a critical refinery operation. In the 1980s, Texaco developed OMEGA, an opti... more Gasoline blending is a critical refinery operation. In the 1980s, Texaco developed OMEGA, an optimization-based decision support system, to assist in planning and scheduling its blending operations. OMEGA ran primarily on minicomputers and on a mainframe computer system. In 1990, Texaco began replacing OMEGA with StarBlend, a Microsoft Windows application, running on personal computers and client-server networks. StarBlend uses a multi-period extension of OMEGA’s blending model written in the GAMS modeling language and extracts model data from relational databases. Its improved features make it easier to use and it enables blenders and blend planners to more readily incorporate future requirements into current blending decisions. Currently, StarBlend is operational in all Texaco refineries. As federal and state regulations on auto emissions become more complex, StarBlend’s importance will continue to increase.
This paper describes modifications to two multistart algorithms for global optimization which ena... more This paper describes modifications to two multistart algorithms for global optimization which enable them to find feasible solutions to a system of nonlinear constraints more efficiently. The multistart algorithms, called OptQuest-NLP (OQNLP) and Multistart-NLP (MSNLP), start a local NLP Solver from a set of starting points and return the best solution found. Candidate starting points are generated either by a scatter search heuristic or by a randomized process. Two adaptive filters choose a small subset of the candidate points as starting points. The modifications to facilitate feasibility seeking include replacing the exact penalty function used to measure the goodness of a starting point with the sum of infeasibilities, and terminating when a feasible solution is found. We describe experimental results on a large and diverse set of smooth nonlinear nonconvex problems coded in the GAMS modeling language. These are chosen so that a single application of a selected solver from the user-specified starting point terminates infeasible, yet the problems all have feasible solutions. Our results show that MSNLP's feasibility mode is able to find feasible solutions to almost all problems. It is moderately faster than MSNLP not using feasibility mode, and is somewhat better a finding feasible solutions when they exist. It is now an option within MSNLP, and can be invoked by inserting an appropriate record into the options file.
Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objec... more Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objectives and constraints. However, in large and highly nonlinear models, these algorithms can fail to ®nd feasible solutions, or converge to local solutions which are not global. Evolutionary search procedures in general, and genetic algorithms (GAs) speci®cally, are less susceptible to the presence of local solutions. However, they often exhibit slow convergence, especially when there are many variables, and have problems ®nding feasible solutions in constrained problems with``narrow'' feasible regions. In this paper, we describe strategies for solving large nonlinear water resources models management, which combine GAs with linear programming. The key idea is to identify a set of complicating variables in the model which, when ®xed, render the problem linear in the remaining variables. The complicating variables are then varied by a GA. This GA&LP approach is applied to two nonlinear models: a reservoir operation model with nonlinear hydropower generation equations and nonlinear reservoir topologic equations, and a long-term dynamic river basin planning model with a large number of nonlinear relationships. For smaller instances of the reservoir model, the CONOPT2 nonlinear solver is more accurate and faster, but for larger instances, the GA&LP approach ®nds solutions with signi®cantly better objective values. The multiperiod river basin model is much too large to be solved in its entirety. The complicating variables are chosen here so that, when they are ®xed, each period's model is linear, and these models can be solved sequentially. This approach allows sucient model detail to be retained so that long-term sustainability issues can be explored.
IEEE Transactions on Systems Science and Cybernetics, 1968
The problem considered is that of obtaining solutions to large nonlinear mathematical programs by... more The problem considered is that of obtaining solutions to large nonlinear mathematical programs by coordinated solution of smaller subproblems. If all functions in the original problem are additively separable, this can be done by finding a saddle point for the associated Lagrangian function. Coordination is then accomplished by shadow prices, with these prices chosen to solve a dual program. Characteristics of the dual program are investigated, and an algorithm is proposed in which subproblems are solved for given shadow prices. These solutions provide the value and gradient of the dual function, and this information is used to update the shadow prices so that the dual problem is brought closer to solution. Application to two classes of problems is given. The first class is one whose constraints describe a system of coupled subsystems; the second is a class of multi-item inventory problems whose decision variables may be discrete.
Several factors imply an increase in the use of nonlinear optimization models. We face serious pr... more Several factors imply an increase in the use of nonlinear optimization models. We face serious problems of declining productivity and increasingly scarce, expensive raw materials. Computers are becoming cheaper and faster, and more efficient nonlinear programming (NLP) algorithms are being developed. This paper attempts to illustrate the potential of NLP by describing the application of nonlinear programming models to three classes of problems: petrochemical industry applications, nonlinear networks, and economic planning. Problems in the petrochemical industry ranging from product blending, refinery unit optimization, and unit design to multiplant production, and distribution planning are discussed. The nonlinear networks topic includes electric power dispatch, hydroelectric reservoir management, and problems involving traffic flow in urban transportation networks. In economic planning, we describe NLP applications involving large dynamic econometric models, a variety of static equ...
This paper reports on progress in nonlinear programming software since 1979. Developments in the ... more This paper reports on progress in nonlinear programming software since 1979. Developments in the computer industry have had a significant impact on the design of mathematical software and the expectations of users. Microcomputers in particular are changing the software industry to an extent that was not anticipated in the last survey. Continuing refinements in NLP algorithms have enabled users to solve larger and more complicated problems, even some with integer variables. Modeling systems with nonlinear programming capabilities have now become available. Interest and improvements in computational experimentation have increased the rigor and objectivity of studies assessing software quality. This report surveys these important developments and speculates on the future.
IEEE Transactions on Systems, Man, and Cybernetics, 1971
The content of this very interesting book is developed in 26 chapters and one appendix. The scope... more The content of this very interesting book is developed in 26 chapters and one appendix. The scope is very broad: the author advances an exhaustive treatment of the nodal analysis of power systems, as considered and developed for the past two decades by the writer and others ...
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Papers by Leon Lasdon