Decomposition branch and bound method for globally solving linearly constrained indefinite quadratic minimization problems

Authors:
Thai Quynh Phong;Le Thi Hoai An;Pham Dinh Tao
Affiliations:
LMI-INSA Rouen, Place Emile Blondel, B. P. 08, 76131 Mont Saint Aignan Cedex, France;LMI-INSA Rouen, Place Emile Blondel, B. P. 08, 76131 Mont Saint Aignan Cedex, France;LMI-INSA Rouen, Place Emile Blondel, B. P. 08, 76131 Mont Saint Aignan Cedex, France
Venue:
Operations Research Letters
Year:
1995

Citing 5
Cited 13

Constrained global optimization: algorithms and applications

Constrained global optimization: algorithms and applications
Global minimization of indefinite quadratic problems

Computing
A collection of test problems for constrained global optimization algorithms

A collection of test problems for constrained global optimization algorithms
Primal-relaxed dual global optimization approach

Journal of Optimization Theory and Applications
Decomposition methods for solving a class of nonconvex programming problems dealing with bilinear and quadratic functions

Computational Optimization and Applications

Maximization of the Ratio of Two Convex Quadratic Functions over a Polytope

Computational Optimization and Applications
A Reduced Space Branch and Bound Algorithm for Globaloptimization

Journal of Global Optimization
A Branch and Bound Algorithm for Solving Low Rank Linear Multiplicative and Fractional Programming Problems

Journal of Global Optimization
Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints

Journal of Global Optimization
Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

Computational Optimization and Applications
Global Optimization Versus Integer Programming in Portfolio Optimization under Nonconvex Transaction Costs

Journal of Global Optimization
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*

Journal of Global Optimization
Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

Journal of Global Optimization
A Response Surface Approach to Beam Orientation Optimization in Intensity-Modulated Radiation Therapy Treatment Planning

INFORMS Journal on Computing
DC programming techniques for solving a class of nonlinear bilevel programs

Journal of Global Optimization
A branch and reduce approach for solving a class of low rank d.c. programs

Journal of Computational and Applied Mathematics
An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs

Journal of Global Optimization
Solving a class of low rank d.c. programs via a branch and bound approach: A computational experience

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

A decomposition branch and bound approach is considered for the global minimization of an indefinite quadratic function over a polytope. The objective function is a sum of a nonseparable convex part and a separable concave part. In many large-scale problems the number of convex variables is much larger than that of concave variables. Taking advantage of this we use a branch and bound method where branching proceeds by rectangular subdivision of the subspace of concave variables. With the help of an easily constructed convex underestimator of the objective function, a lower bound is obtained by solving a convex quadratic programming problem. Three variants using exhaustive, adaptive and w-subdivision are discussed. Computational results are presented for problems with 10-20 concave variables and up to 200 convex variables.