Yaguang Yang

Arc-Search Techniques for Interior-Point Methods (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 316
• Erscheinungstermin: 26. November 2020
• Englisch
• ISBN-13: 9781000220339
• Artikelnr.: 60167577

Autorenporträt

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.

Inhaltsangabe

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.