A global optimization algorithm using parametric linearization relaxation

In this paper a global optimization algorithm based on a parametric linearizing method for generalized quadratic programming (GQP), i.e., the quadratic programming problem with nonconvex quadratic constraints, is proposed. By utilizing the linearizing method initial nonconvex nonlinear problem GQP is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region and of the objective function. The proposed algorithm is convergent to the global minimum of GQP by means of the subsequent solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of GQP on a microcomputer.

[1]  Tim Van Voorhis,et al.  A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method , 2002, J. Glob. Optim..

[2]  Costas D. Maranas,et al.  Global Optimization in Generalized Geometric Programming , 1997, Encyclopedia of Optimization.

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

[4]  R. Sargent.  Primal-Relaxed Dual Global Optimization Approach , 2022 .

[5]  Reiner Horst,et al.  Convergent Outer Approximation Algorithms for Solving Unary Programs , 1996, J. Glob. Optim..

[6]  Mustafa Khammash,et al.  Synthesis of globally optimal controllers for robust performance to unstructured uncertainty , 1996, IEEE Trans. Autom. Control..

[7]  C. Floudas,et al.  Global Optimization in Generalized Geometric Programming , 1997, Encyclopedia of Optimization.

[8]  Ya-Xiang Yuan,et al.  Optimality Conditions for the Minimization of a Quadratic with Two Quadratic Constraints , 1997, SIAM J. Optim..

[9]  Le Thi Hoai An,et al.  An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints , 2000, Math. Program..

[10]  Yinyu Ye,et al.  Approximating Global Quadratic Optimization with Convex Quadratic Constraints , 1999, J. Glob. Optim..

[11]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

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

[13]  Faiz A. Al-Khayyal,et al.  Difference of convex solution of quadratically constrained optimization problems , 2003, Eur. J. Oper. Res..