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Arc-search techniques for interior-point methods [electronic resource] / Yaguang Yang.

By: Yang, Yaguang [author.].
Material type: materialTypeLabelBookPublisher: Boca Raton : CRC Press ; Taylor & Francis Group, [2020]Description: 1 online resource.Content type: text | still image Media type: computer Carrier type: online resourceISBN: 9781000220339; 1000220338; 9781000220131; 1000220133; 9781000220230; 1000220230; 9781003042518; 1003042511.Subject(s): Interior-point methods | Linear programming | Computer algorithms | MATHEMATICS / Applied | MATHEMATICS / Arithmetic | MATHEMATICS / Graphic MethodsDDC classification: 519.7 Online resources: Taylor & Francis | OCLC metadata license agreement
Contents:
A potential-reduction algorithm for LP -- Feasible path-following algorithms for LP -- Infeasible interior-point method algorithms for LP -- 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( n̄L) infeasible arc-search algorithm for LP -- An arc-search algorithm for convex quadratic programming -- An arc-search algorithm for QP with box constraints -- An arc-search algorithm for LCP -- An arc-search algorithm for semidefinite programming.
Summary: "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, i.e., the algorithm with the best polynomial bound is the least efficient and the most efficient interior-point algorithm cannot be proved to converge. The book also covers important results since 1990s and the extensions of the arc-search techniques to the general optimization problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming"-- Provided by publisher.
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A potential-reduction algorithm for LP -- Feasible path-following algorithms for LP -- Infeasible interior-point method algorithms for LP -- 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( n̄L) infeasible arc-search algorithm for LP -- An arc-search algorithm for convex quadratic programming -- An arc-search algorithm for QP with box constraints -- An arc-search algorithm for LCP -- An arc-search algorithm for semidefinite programming.

"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, i.e., the algorithm with the best polynomial bound is the least efficient and the most efficient interior-point algorithm cannot be proved to converge. The book also covers important results since 1990s and the extensions of the arc-search techniques to the general optimization problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming"-- Provided by publisher.

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