Alternating direction method for bi-quadratic programming

Authors:
Sheng-Long Hu;Zheng-Hai Huang
Affiliations:
Department of Mathematics, School of Science, Tianjin University, Tianjin, People's Republic of China 300072 and Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, ...;Department of Mathematics, School of Science, Tianjin University, Tianjin, People's Republic of China 300072
Venue:
Journal of Global Optimization
Year:
2011

Citing 16
Cited 0

On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators

Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems

Mathematical Programming: Series A and B
Independent component analysis, a new concept?

Signal Processing - Special issue on higher order statistics
A variable-penalty alternating directions method for convex optimization

Mathematical Programming: Series A and B
High-order contrasts for independent component analysis

Neural Computation
Tensor displacement structures and polyspectral matching

Fast reliable algorithms for matrices with structure
Rank-One Approximation to High Order Tensors

SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors

SIAM Journal on Matrix Analysis and Applications
On cones of nonnegative quadratic functions

Mathematics of Operations Research
Some Properties of the Augmented Lagrangian in Cone Constrained Optimization

Mathematics of Operations Research
Solving semidefinite programming problems via alternating direction methods

Journal of Computational and Applied Mathematics
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
Standard bi-quadratic optimization problems and unconstrained polynomial reformulations

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bi-quadratic programming (Bi-QP for short) was studied systematically in Ling et al. (SIAM J. Optim. 20:1286---1320, 2009) due to its various applications in engineering as well as optimization. Several approximation methods were given in the same paper since it is NP-hard. In this paper, we introduce a quadratic SDP relaxation of Bi-QP and discuss the approximation ratio of the method. In particular, by exploiting the favorite structure of the quadratic SDP relaxation, we propose an alternating direction method for solving such a problem and show that the method is globally convergent without any assumption. Some preliminary numerical results are reported which show the effectiveness of the method proposed in this paper.