Development of Algorithms for Solving Minimizing Problems with Convex Quadratic Function on Special Convex Sets and Applications

Abstract

The thesis focuses on solving the optimization problems of a minimization a convex quadratic function on a special convex set. Such problems appear in many engineering applications, e.g., in the solution of contact problems of elasticity or in particle dynamics simulations. The number of unknows in these practical problems usually exceeds the potential of sequential algorithms. In the thesis, we present iterative methods which can be easily parallelizable. The text is divided into three parts; the review of the basic quadratic programming theory, the algorithms for solving the problem, and the numerical experiments. We demonstrate and compare the efficiency of the algorithms on the solution of benchmarks with millions unknowns solved at the Anselm supercomputer of the IT4Innovations National Supercomputing Center.