Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures

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

Hybrid methods for nonlinear least squares problems

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

Numerical solution of generalized minimax problems

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

Optimization Methods for Large-Scale Machine Learning

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

UFO 2014 – Interactive System for Universal Functional Optimization

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. Citation Research Report V1218-14, Institute of Computer Science, Czech Academy of Sciences, Prague 2014. Article Download View UFO 2014 – Interactive System for Universal Functional Optimization

Nonconvex Robust Optimization

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

Computational experience with modified conjugate gradient methods for unconstrained optimization

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. Citation Technical report No. 1038, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008 Article Download View Computational experience … Read more

Derivative Free Optimization Methods for Optimizing Stirrer Configurations

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

A New Stochastic Algorithm for Engineering Optimization Problems

This paper proposes a new stochastic algorithm, Search via Probability (SP) algorithm, for single-objective optimization problems. The SP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each iteration, and on the performance of SP algorithm we … Read more

Parallel Computing on Semidefinite Programs

This paper demonstrates how interior-point methods can use multiple processors efficiently to solve large semidefinite programs that arise in VLSI design, control theory, and graph coloring. Previous implementations of these methods have been restricted to a single processor. By computing and solving the Schur complement matrix in parallel, multiple processors enable the faster solution of … Read more