Arc-Search Techniques for Interior-Point Methods

ISBN-13: 9780367510091 / Angielski / Miękka / 2022 / 306 str.

Yaguang Yang

Opis

This book discusses one of the most recent developments in interior-point methods, the arc-search techniques. Introducing these techniques result in an efficient interior-point algorithm with the lowest polynomial bound, which solves a long-standing issue of the interior-point methods in linear programming.

Spis treści

Preface. SECTION I: LINE SEARCH INTERIOR-POINT METHODS FOR LINEAR PROGRAMMING. Introduction. A Potential-Reduction Algorithm for LP. Feasible Path-Following Algorithms for LP. Infeasible Interior-Point Method Algorithms for LP. SECTION II: ARC-SEARCH INTERIOR-POINT METHODS FOR LINEAR PROGRAMMING. A Feasible Arc-Search Algorithm for LP. A MTY-Type Infeasible Arc-Search Algorithm for LP. A Mehrotra-Type Infeasible Arc-Search Algorithm for LP. An O(√nL) Infeasible Arc-Search Algorithms for LP. SECTION III:ARC-SEARCH INTERIOR-POINT METHODS: EXTENSIONS. An Arc-Search Algorithm for Convex Quadratic Programming. An Arc-Search Algorithms for QP with Box Constraints. An Arc-Search Algorithm for LCP. An Arc-Search Algorithm for Semidefinite Programming. References. Index.