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题名/责任者:

Low-rank semidefinite programming : theory and programming / Alex Lemon, Anthony Man-Cho, Yinyu Ye.

出版发行项:

Hanover, MA : Now Publishers Inc., 2016.

ISBN:

9781680831368 (pbk.)

ISBN:

1680831364 (pbk.)

载体形态项:

xi, 166 p. : ill. ; 24 cm.

丛编说明:

Foundations and trends in optimization, 2167-3888 ; v. l2, Iss. 1-2

个人责任者:

Lemon, Alex.

附加个人名称:

So, Anthony Man-Cho1

论题主题:

Semidefinite programming.

论题主题:

Mathematical optimization.

中图法分类号:

O224

书目附注:

Includes bibliographical references (p. 159-166)

摘要附注:

Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. In this paper we review the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. Then we present applications of the theory to trust-region problems and signal processing.

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