Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
The complexity of approximating a nonlinear program
Mathematical Programming: Series A and B
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
On Standard Quadratic Optimization Problems
Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
D.C. Versus Copositive Bounds for Standard QP
Journal of Global Optimization
A PTAS for the minimization of polynomials of fixed degree over the simplex
Theoretical Computer Science - Approximation and online algorithms
A linear programming reformulation of the standard quadratic optimization problem
Journal of Global Optimization
A bilinear formulation for vector sparsity optimization
Signal Processing
A clique algorithm for standard quadratic programming
Discrete Applied Mathematics
Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation
Computational Optimization and Applications
A dynamic cost weighting framework for unit selection text-to-speech synthesis
IEEE Transactions on Audio, Speech, and Language Processing
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
A Variational Approach to Copositive Matrices
SIAM Review
SIAM Journal on Optimization
Journal of Global Optimization
Semidefinite bounds for the stability number of a graph via sums of squares of polynomials
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
An improved algorithm to test copositivity
Journal of Global Optimization
Journal of Global Optimization
Dense Neighborhoods on Affinity Graph
International Journal of Computer Vision
Exploiting equalities in polynomial programming
Operations Research Letters
Approximation algorithm for a class of global optimization problems
Journal of Global Optimization
Tightening a copositive relaxation for standard quadratic optimization problems
Computational Optimization and Applications
A note on set-semidefinite relaxations of nonconvex quadratic programs
Journal of Global Optimization
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The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities (LMI's). In particular, we show that our approach leads to a polynomial-time approximation scheme for the standard quadratic optimzation problem. This is an improvement on the previous complexity result by Nesterov who showed that a 2/3-approximation is always possible. Numerical examples from various applications are provided to illustrate our approach.