In this paper we propose a new algorithm for solving a class of nonsmooth nonconvex problems, which is obtained by combining the iteratively reweighted scheme with a finite number of forward–backward iterations based on a linesearch procedure. The new method overcomes some limitations of linesearch forward–backward methods, since it can be applied also to minimize … Read more
The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we … Read more
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function $F(x) = (1/2) f^T(x) f(x)$, where $x \in R^n$ and $f \in R^m$, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved … Read more
This contribution contains the description and investigation of four numerical methods for solving generalized minimax problems, which consists in the minimization of functions which are compositions of special smooth convex functions with maxima of smooth functions (the most important problem of this type is the sum of maxima of smooth functions). Section~1 is introductory. In … Read more
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of … Read more
This report contains a description of the interactive system for universal functional optimization UFO, version 2014. This version contains interfaces to the MATLAB and SCILAB graphics environments. CitationResearch Report V1218-14, Institute of Computer Science, Czech Academy of Sciences, Prague 2014. ArticleDownload View PDF
We propose a novel robust optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems are nonconvex and involve computer-based simulations. In these applications, the relationship between decision … Read more
In this report, several modifications of the nonlinear conjugate gradient method are described and investigated. Theoretical properties of these modifications are proved and their practical performance is demonstrated using extensive numerical experiments. CitationTechnical report No. 1038, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008ArticleDownload View PDF
In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method … Read more