Arc-Search Techniques for Interior-Point Methods - Yaguang Yang

Arc-Search Techniques for Interior-Point Methods

(Autor)

Buch | Hardcover
316 Seiten
2020
CRC Press (Verlag)
978-0-367-48728-7 (ISBN)
168,35 inkl. MwSt
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.
This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method.

This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.

Yaguang Yang received a BSc (1982) and a MSc (1985) from Huazhong University of Science and Technology, China. From 1985 to 1990, he was a lecturer at Zhejiang University in China. In 1996, he received his PhD from the Department of Electrical and Computer Engineering at the University of Maryland, College Park. He proposed and developed arc-search techniques for interior-point methods. He is currently with the US Nuclear Regulatory Commission.

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.

Erscheinungsdatum
Zusatzinfo 6 Tables, black and white; 11 Illustrations, color
Verlagsort London
Sprache englisch
Maße 156 x 234 mm
Gewicht 739 g
Themenwelt Informatik Theorie / Studium Algorithmen
Mathematik / Informatik Mathematik Angewandte Mathematik
ISBN-10 0-367-48728-4 / 0367487284
ISBN-13 978-0-367-48728-7 / 9780367487287
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich
Interlingua zur Gewährleistung semantischer Interoperabilität in der …

von Josef Ingenerf; Cora Drenkhahn

Buch | Softcover (2023)
Springer Fachmedien (Verlag)
32,99