Papers by Bartlomiej Kubica
The paper presents the first author's C++ library ADHC for algorithmic differentiation and hu... more The paper presents the first author's C++ library ADHC for algorithmic differentiation and hull consistency enforcing using interval calculus. The code is based on C++ templates, so that the same source code could be used to generate binary functions for various cases: for evaluating the function value, its various derivatives or creating expression tree to enforce hull consistency. Also, we can choose at compile-time to use sparse or dense containers for higher derivatives. Preliminary experiments are reported.
Studies in computational intelligence, 2019
The series "Studies in Computational Intelligence" (SCI) publishes new developments and advances ... more The series "Studies in Computational Intelligence" (SCI) publishes new developments and advances in the various areas of computational intelligence-quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the worldwide distribution, which enable both wide and rapid dissemination of research output. The books of this series are submitted to indexing to Web of Science, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink.
Springer eBooks, 2020
One of the important steps in deep learning is softmax, when we select one of the alternatives wi... more One of the important steps in deep learning is softmax, when we select one of the alternatives with a probability depending on its expected gain. A similar formula describes human decision making: somewhat surprisingly, when presented with several choices with different expected equivalent monetary gain, we do not just select the alternative with the largest gain; instead, we make a random choice, with probability decreasing with the gain-so that it is possible that we will select second highest and even third highest value. Both formulas assume that we know the exact value of the expected gain for each alternative. In practice, we usually know this gain only with some uncertainty. For example, often, we only know the lower bound f and the upper bound f on the expected gain, i.e., we only know that the actual gain f is somewhere in the interval [f , f ]. In this paper, we show how to extend softmax and discrete choice formulas to such cases of interval uncertainty.
Prace Naukowe Politechniki Warszawskiej. Elektronika, 2008
Studies in computational intelligence, 2020
Journal of Parallel and Distributed Computing, Sep 1, 2017
h i g h l i g h t s • We describe incorporating bound-consistency enforcing into an interval solv... more h i g h l i g h t s • We describe incorporating bound-consistency enforcing into an interval solver. • We investigate a few versions of parallelization of this procedure. • Heuristics and policies for using the procedure are developed. • Numerical results on multi-core and many-core architectures are presented.
Numerical Algorithms
Algorithmic differentiation is a tool used in several branches of computational science, both in ... more Algorithmic differentiation is a tool used in several branches of computational science, both in conjunction with the interval calculus, and apart of it. This paper presents the ADHC library [14] developed by the author, and identified as package “na60” by Numerical Algorithms journal. This library makes intensive use of the C++ template meta-programming, and it has several unique features. ADHC seems particularly useful for interval-related applications. The library has been used by some solvers, also developed by the author, including HIBA_USNE. The paper describes the library, presenting its features, focusing on the new ones, added in version 2.0; in particular, we describe bounding subdifferentials of non-smooth functions and computing derivatives over various datatypes. Efficiency comparison with respect to other packages is also presented. Then some examples of ADHC applications are given, involving the use of HIBA_USNE and standard benchmark problems for solving nonlinear sy...
Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems, 2019
This chapter presents implementation details of B&BT algorithms. We consider several tools an... more This chapter presents implementation details of B&BT algorithms. We consider several tools and features: data structures, memory management and, most notably, parallelization. Both shared-memory and distributed-memory environments are considered. Issues of both cases are discussed. Promising future directions are outlined, also.
In this paper, we show how to take interval uncertainty into account when solving conflict situat... more In this paper, we show how to take interval uncertainty into account when solving conflict situations. Algorithms for conflict situations under interval uncertainty are known under the assumption that each side of the conflict maximizes its worst-case expected gain. However, it is known that a more general Hurwicz approach provides a more adequate description of decision making under uncertainty. In this approach, each side maximizes the convex combination of the worst-case and the best-case expected gains. In this paper, we describe how to resolve conflict situations under the general Hurwicz approach to interval uncertainty.
Lecture Notes in Computer Science, 2007
We present an interval global optimization algorithm using a modified monotonicity test. The impr... more We present an interval global optimization algorithm using a modified monotonicity test. The improvement applies to constrained problems and can result in significant speedup, when constraints are sparse, i.e. they "bind" a few of the variables, not all of them. A theorem that ensures the correctness of the new tool, is given and proved. The improved method is applied to an economic problem of setting optimal prices on a couple of products.
Decision Making in Manufacturing and Services, 2015
The problem of seeking strong Nash equilibria of a continuous game is considered. For some games,... more The problem of seeking strong Nash equilibria of a continuous game is considered. For some games, these points cannot be found analytically, only numerically. Interval methods provide us with an approach to rigorously verify the existence of equilibria in certain points. A proper algorithm is presented. We formulate and prove propositions, that give us features which have to be used by the algorithm (to the best knowledge of the authors, these propositions and properties are original). Parallelization of the algorithm is also considered, and numerical results are presented. As a particular example, we consider the game of "misanthropic individuals", a game, invented by the first author, that may have several strong Nash equilibria depending on the number of players. Our algorithm is able to localize and verify these equilibria.
The paper describes a new algorithm for verifying solutions of nonlinear systems of equations. In... more The paper describes a new algorithm for verifying solutions of nonlinear systems of equations. Interval methods provide us a few tools for such verification. Some of them are based on topological theorems. Also our new test is based on checking the extendability of the function from a subspace of the boundary of the box to its interior. For a system of two equations, we can provide an efficient implementation. Generalization to a higher number of equations is also theoretically possible, yet cumbersome. Some numerical results are presented.
This paper considers the problem of numerical computation of a definite integral of the entropy d... more This paper considers the problem of numerical computation of a definite integral of the entropy density function over a wide, potentially unbounded, domain. Despite there are efficient approaches to compute the quadrature over a finite (hyper)rectangle, it may be challenging to bound the whole domain, out of which the function is negligible. An approach based on the interval analysis is proposed in this paper. Preliminary numerical results are also discussed.
Journal of telecommunications and information technology, 2011
The paper presents an idea to use weak derivatives in interval global optimization. It allows usi... more The paper presents an idea to use weak derivatives in interval global optimization. It allows using the Newton operator to narrow domains of non-differentiable functions. Preliminary computational experiments are also presented. Keywords—Dirac delta, distributions, generalized derivative, interval computations, interval Newton method, non-differentiable optimization.
This paper considers the shared-memory parallelization of an interval solver of underdetermined s... more This paper considers the shared-memory parallelization of an interval solver of underdetermined systems of nonlinear equations. Four threading libraries are investigated: OpenMP, POSIX threads, Boost threads and TBB. Directions for further investigations on multi-threaded interval algorithms are outlined.
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Papers by Bartlomiej Kubica