On solving biquadratic optimization via semidefinite relaxation

Authors:
Yuning Yang;Qingzhi Yang
Affiliations:
School of Mathematics Science and LPMC, Nankai University, Tianjin, P.R. China 300071;School of Mathematics Science and LPMC, Nankai University, Tianjin, P.R. China 300071
Venue:
Computational Optimization and Applications
Year:
2012

Citing 17
Cited 0

Independent component analysis, a new concept?

Signal Processing - Special issue on higher order statistics
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM (JACM)
High-order contrasts for independent component analysis

Neural Computation
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors

SIAM Journal on Matrix Analysis and Applications
Global Optimization with Polynomials and the Problem of Moments

SIAM Journal on Optimization
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations

Computational Optimization and Applications
Approximating the Cut-Norm via Grothendieck's Inequality

SIAM Journal on Computing
Z-eigenvalue methods for a global polynomial optimization problem

Mathematical Programming: Series A and B
Linear Equations Modulo 2 and the $L_1$ Diameter of Convex Bodies

SIAM Journal on Computing
Tensor Decompositions and Applications

SIAM Review
Eigenvalues of a real supersymmetric tensor

Journal of Symbolic Computation
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Approximation algorithms for homogeneous polynomial optimization with quadratic constraints

Mathematical Programming: Series A and B - 20th International Symposium on Mathematical Programming – ISMP 2009
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations

SIAM Journal on Optimization
A Semidefinite Relaxation Scheme for Multivariate Quartic Polynomial Optimization with Quadratic Constraints

SIAM Journal on Optimization
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints

Journal of Global Optimization
Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems

Mathematical Programming: Series A and B - Special Issue on Large Scale Optimization: Analysis, Algorithms and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several different constraints, we present variational approaches for solving them and give provable estimation for the approximation solutions. Some numerical results are reported at the end of this paper.