Comparison of Lasserre's Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing

被引：14

作者：

De Klerk, Etienne ^{[1
,2
]}

Laurent, Monique ^{[1
,3
]}

机构：

[1] Tilburg Univ, NL-5000 LE Tilburg, Netherlands

[2] Delft Univ Technol, NL-2600 AA Delft, Netherlands

[3] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2018年 / 43卷 / 04期

关键词：

polynomial optimization; semidefinite optimization; Lasserre hierarchy; simulated annealing;

D O I：

10.1287/moor.2017.0906

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider the problem of minimizing a continuous function f over a compact set K. We compare the hierarchy of upper bounds proposed by Lasserre [Lasserre JB (2011) A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21(3): 864-885] to bounds that may be obtained from simulated annealing. We show that, when f is a polynomial and K a convex body, this comparison yields a faster rate of convergence of the Lasserre hierarchy than what was previously known in the literature.

引用

页码：1317 / 1325

页数：9

共 16 条

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