Solving Euclidean distance matrix completion problems via semidefinite programming

被引：144

作者：

Alfakih, AY ^{[1
]}

Khandani, A

Wolkowicz, H

机构：

[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

[2] Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 1999年 / 12卷 / 1-3期

关键词：

Euclidean distance matrices; semidefinite programming; completion problems; primal-dual interior-point method;

D O I：

10.1023/A:1008655427845

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：

Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (EDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (EDM). In this paper, we follow the successful approach in [20] and solve the EDMCP by generalizing the completion problem to allow for approximate completions. In particular, we introduce a primal-dual interior-point algorithm that solves an equivalent (quadratic objective function) semidefinite programming problem (SDP). Numerical results are included which illustrate the efficiency and robustness of our approach. Our randomly generated problems consistently resulted in low dimensional solutions when no completion existed.

引用

页码：13 / 30

页数：18

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