KKT Solution and Conic Relaxation for Solving Quadratically Constrained Quadratic Programming Problems

To find a global optimal solution to the quadratically constrained quadratic programming problem, we explore the relationship between its Lagrangian multipliers and related linear conic programming problems. This study leads to a global optimality condition that is more general than the known positi...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 21; no. 4; pp. 1475 - 1490
Main Authors: Lu, Cheng, Fang, Shu-Cherng, Jin, Qingwei, Wang, Zhenbo, Xing, Wenxun
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.10.2011
Subjects:
Algorithms
Approximation
Optimization
Quadratic programming
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:To find a global optimal solution to the quadratically constrained quadratic programming problem, we explore the relationship between its Lagrangian multipliers and related linear conic programming problems. This study leads to a global optimality condition that is more general than the known positive semidefiniteness condition in the literature. Moreover, we propose a computational scheme that provides clues of designing effective algorithms for more solvable quadratically constrained quadratic programming problems. [PUBLICATION ABSTRACT]
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ISSN:1052-6234
1095-7189
DOI:10.1137/100793955