Unbounded convex sets for non-convex mixed-integer quadratic programming

被引：7

作者：

Burer, Samuel ^{[1
]}

Letchford, Adam N. ^{[2
]}

机构：

[1] Univ Iowa, Dept Management Sci, Tippie Coll Business, Iowa City, IA 52242 USA

[2] Univ Lancaster, Dept Management Sci, Lancaster, England

来源：

MATHEMATICAL PROGRAMMING | 2014年 / 143卷 / 1-2期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Mixed-integer non-linear programming; Global optimisation; Polyhedral combinatorics; Convex analysis; BOX CONSTRAINTS; SEMIDEFINITE; OPTIMIZATION; RELAXATION; POLYTOPE; MATRICES;

D O I：

10.1007/s10107-012-0609-9

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a face of a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some other well-studied convex sets. Several classes of valid and facet-inducing inequalities are also derived.

引用

页码：231 / 256

页数：26

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