New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming
| Autor: | Mohand Bentobache, Mohamed Telli, Abdelkader Mokhtari |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Control and Optimization
Applied Mathematics Successive linear programming MathematicsofComputing_NUMERICALANALYSIS Management Science and Operations Research Computer Science Applications Domain (software engineering) Quadratic equation Simplex algorithm Convex polytope Quadratic programming Extreme point Algorithm Mathematics Integer (computer science) |
| Zdroj: | Journal of Global Optimization. 82:659-689 |
| ISSN: | 1573-2916 0925-5001 |
| DOI: | 10.1007/s10898-021-01108-w |
| Popis: | In this work, we propose a new approach called “Successive Linear Programming Algorithm (SLPA)” for finding an approximate global minimizer of general nonconvex quadratic programs. This algorithm can be initialized by any extreme point of the convex polyhedron of the feasible domain. Furthermore, we generalize the simplex algorithm for finding a local minimizer of concave quadratic programs written in standard form. We prove a new necessary and sufficient condition for local optimality, then we describe the Revised Primal Simplex Algorithm (RPSA). Finally, we propose a hybrid local-global algorithm called “SLPLEX”, which combines RPSA with SLPA for solving general concave quadratic programs. In order to compare the proposed algorithms to the branch-and-bound algorithm of CPLEX12.8 and the branch-and-cut algorithm of Quadproga, we develop an implementation with MATLAB and we present numerical experiments on 139 nonconvex quadratic test problems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink