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2011•SIAM Journal on OptimizationRequires access

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

Cheng Lü, Shu‐Cherng Fang, Qingwei Jin, Zhenbo Wang, Wenxun Xing

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Quadratic growth, Karush–Kuhn–Tucker conditions, Mathematics, Quadratic programming, Quadratically constrained quadratic program, Conic section, Relaxation (psychology), Second-order cone programming

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