Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization

被引：6

作者：

Arima, Naohiko ^{[1
]}

Kim, Sunyoung ^{[2
]}

Kojima, Masakazu ^{[3
]}

机构：

[1] Tokyo Inst Technol, Tokyo 152, Japan

[2] Ewha W Univ, Seoul, South Korea

[3] Chuo Univ, Tokyo 112, Japan

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2016年 / 168卷 / 03期

关键词：

Moment cone relaxation; Polynomial optimization; Copositive programming; Completely positive programming; BINARY;

D O I：

10.1007/s10957-015-0794-9

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 propose the moment cone relaxation for a class of polynomial optimization problems to extend the results on the completely positive cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.

引用

页码：884 / 900

页数：17

共 11 条

[1]

Arima N, 2014, PAC J OPTIM, V10, P437

[2] A QUADRATICALLY CONSTRAINED QUADRATIC OPTIMIZATION MODEL FOR COMPLETELY POSITIVE CONE PROGRAMMING [J].