A new bound-and-reduce approach of nonconvex quadratic programming problems

Abstract For the nonconvex quadratic programming problem, a new linear programming relaxation bound-and-reduce algorithm is proposed and its convergence is proved. In this algorithm, a new hyper-rectangle partition technique and a new linear programming relaxation tactics are used. At the same time, the hyper-rectangular reduction method is used to raise its convergent speed. The numerical results demonstrate the effectiveness and feasibility of the proposed algorithm.

[1]  Peiping Shen,et al.  Global optimization of signomial geometric programming using linear relaxation , 2004, Appl. Math. Comput..

[2]  H. Tuy.  Global Minimization of a Difference of Two Convex Functions , 1987 .

[3]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[4]  Nikolaos V. Sahinidis,et al.  Global Optimization of Multiplicative Programs , 2003, J. Glob. Optim..

[5]  Katta G. Murty,et al.  Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..

[6]  Weldon A. Lodwick,et al.  Preprocessing Nonlinear Functional Constraints with Applications to the Pooling Problem , 1992, INFORMS J. Comput..

[7]  P. Pardalos,et al.  Checking local optimality in constrained quadratic programming is NP-hard , 1988 .

[8]  Immanuel M. Bomze,et al.  A finite algorithm for solving general quadratic problems , 1994, J. Glob. Optim..

[9]  Nikolaos V. Sahinidis,et al.  A branch-and-reduce approach to global optimization , 1996, J. Glob. Optim..

[10]  Jerzy A. Filar,et al.  Bilinear programming and structured stochastic games , 1985 .

[11]  Oscar Barrientos,et al.  An Algorithm for Global Minimization of Linearly Constrained Quadratic Functions* , 2000, J. Glob. Optim..

[12]  Xi Feng.  A New Branch and Bound Algorithm for Solving Complex Integer Quadratic Programs , 2004 .

[13]  Panos M. Pardalos,et al.  Global minimization of large-scale constrained concave quadratic problems by separable programming , 1986, Math. Program..

[14]  Panos M. Pardalos,et al.  Introduction to Global Optimization , 2000, Introduction to Global Optimization.

[15]  J. Ben Rosen,et al.  A parallel algorithm for constrained concave quadratic global minimization , 1988, Math. Program..

[16]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[17]  Peiping Shen,et al.  Linearization method of global optimization for generalized geometric programming , 2005, Appl. Math. Comput..

[18]  Yuelin Gao,et al.  A new rectangle branch-and-reduce approach for solving nonconvex quadratic programming problems , 2005, Appl. Math. Comput..