Journal:Informatica
Volume 27, Issue 2 (2016), pp. 323–334
Abstract
This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.
Journal:Informatica
Volume 22, Issue 4 (2011), pp. 471–488
Abstract
We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.
Journal:Informatica
Volume 20, Issue 2 (2009), pp. 173–186
Abstract
In this paper, we consider the problem of semi-supervised binary classification by Support Vector Machines (SVM). This problem is explored as an unconstrained and non-smooth optimization task when part of the available data is unlabelled. We apply non-smooth optimization techniques to classification where the objective function considered is non-convex and non-differentiable and so difficult to minimize. We explore and compare the properties of Simulated Annealing and of Simultaneous Perturbation Stochastic Approximation (SPSA) algorithms (SPSA with the Lipschitz Perturbation Operator, SPSA with the Uniform Perturbation Operator, Standard Finite Difference Approximation) for semi-supervised SVM classification. Numerical results are given, obtained by running the proposed methods on several standard test problems drawn from the binary classification literature. The performance of the classifiers were evaluated by analyzing Receiver Operating Characteristics (ROC).
Journal:Informatica
Volume 4, Issues 3-4 (1993), pp. 335–350
Abstract
This paper is devoted to research aspects of the convergence rate of conservative difference schemes (d.s.) with time-adaptive grids in cases, where a space grid is irregular and the third boundary-value problem is considered for one-dimensional linear parabolic equations. The unconditional convergence of created d.s. is proved in a C-metric at the rate O(h2+τ01/2).
Journal:Informatica
Volume 3, Issue 2 (1992), pp. 275–279
Abstract
In some recent papers a discussion on global minimization algorithms for a broad class of functions was started. An idea is presented here why such a case is different from a case of Lipshitzian functions in respect with the convergence and why for a broad class of functions an algorithm converges to global minimum of an objective function if it generates an everywhere dense sequence of trial points.