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• 000 01513nam a2200241 a 4500

• 001 0000846310

• 005 20251107152400.0

• 008 180309s2016 maua b 000 0 eng d

• 020 __ |a 9781680831368 (pbk.)

• 020 __ |a 1680831364 (pbk.)

• 040 __ |a SJT |c SJT

• 090 __ |a O224/X6

• 093 __ |a O224 |2 5

• 100 1_ |a Lemon, Alex.

• 245 10 |a Low-rank semidefinite programming : |b theory and programming / |c Alex Lemon, Anthony Man-Cho, Yinyu Ye.

• 260 __ |a Hanover, MA : |b Now Publishers Inc., |c 2016.

• 300 __ |a xi, 166 p. : |b ill. ; |c 24 cm.

• 490 0_ |a Foundations and trends in optimization, |x 2167-3888 ; |v v. l2, Iss. 1-2

• 504 __ |a Includes bibliographical references (p. 159-166)

• 520 __ |a 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.

• 650 _0 |a Semidefinite programming.

• 650 _0 |a Mathematical optimization.

• 700 1_ |a So, Anthony Man-Cho1