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

Authors:
Cheng Lu;Shu-Cherng Fang;Qingwei Jin;Zhenbo Wang;Wenxun Xing
Affiliations:
c-lu06@mails.tsinghua.edu.cn and zwang@math.tsinghua.edu.cn and wxing@math.tsinghua.edu.cn;fang@ncsu.edu and qingweijin@gmail.com;-;-;-
Venue:
SIAM Journal on Optimization
Year:
2011

Citing 16
Cited 0

On the complexity of approximating a KKT point of quadratic programming

Mathematical Programming: Series A and B
Lectures on modern convex optimization: analysis, algorithms, and engineering applications

Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation of the Stability Number of a Graph via Copositive Programming

SIAM Journal on Optimization
Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

SIAM Journal on Optimization
Optimality Conditions for the Minimization of a Quadratic with Two Quadratic Constraints

SIAM Journal on Optimization
Canonical Dual Transformation Method and Generalized Triality Theory in Nonsmooth Global Optimization*

Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems

Journal of Global Optimization
On cones of nonnegative quadratic functions

Mathematics of Operations Research
Further Results on Approximating Nonconvex Quadratic Optimization by Semidefinite Programming Relaxation

SIAM Journal on Optimization
New Results on Quadratic Minimization

SIAM Journal on Optimization
Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming

Journal of Global Optimization
LMI Approximations for Cones of Positive Semidefinite Forms

SIAM Journal on Optimization
On the gap between the quadratic integer programming problem and its semidefinite relaxation

Mathematical Programming: Series A and B
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions

Mathematical Programming: Series A and B
On the copositive representation of binary and continuous nonconvex quadratic programs

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

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.