Optimization of a Quadratic Function under its Canonical Form

Chikhaoui, Ahmed; Djebbar, Bachir; Belabbaci, Amel; Mokhtari, Abdelkader

doi:10.3923/ajaps.2009.499.510

Cited by 7 publications

(3 citation statements)

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“…From the different tables and graphs, we can make the following remarks: (6) and Globallib (64), SLPA has found the same objective values as those found by CPLEX for 65 test problems and a slightly better value for one problem (st_ph14). For the other four problems, our algorithm found approximate values which are close to the values found by CPLEX.…”

Section: Algorithm 4 (Slplex)mentioning

confidence: 61%

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New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

2021

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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. KeywordsNonconvex quadratic programming • Concave quadratic programming • Successive linear programming • Simplex algorithm • Extreme point • Local minimizer • Global minimizer • Approximate global minimizer • Numerical experiments Mathematics Subject Classification 90C20 • 90C26 • 90C59 B Mohand Bentobache

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Section: Algorithm 4 (Slplex)mentioning

confidence: 61%

“…3a. (6) Eight concave quadratic test problems randomly generated with the algorithm proposed in [36]. These QP problems are written in the form:…”

Section: Algorithm 4 (Slplex)mentioning

confidence: 99%

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

2021

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“…Certainly it can be formulated as a linear program (Chikhaoui et al, 2009), that find the exact solution of a quadratic programming problem with linear constraints of an objective quadratic function written in the canonical form, which is based on splitting the objective function into the sum of two functions. The Lot-size is the clustering of items for transportation or manufacturing processes occurring at the same time.…”

Section: Agorithms For Solvingmentioning

confidence: 99%

The Best Candidates Method for Solving Optimization Problems

Ahmad¹

2012

Journal of Computer Science

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Problem statement:This study is about describing solution technique called Best Candidates Method (BCM) for solving optimization problems; the goal is to minimize the computation time to get the optimal solution. In this study I apply the BCM to the linear assignment problems (LAP) that is one of the optimization problems in the Operation Research (OR). Approach: The optimization problem solution methods operate in two ways. First, that find all available combinations in sequential or parallel solution manner then compare the results to get the optimal one, but its need a very large computation time either for a large scale problems. Second, is to try to reach directly the optimal solution using different methods, but all available methods not always reach the optimal solution and have a complex solution technique or have a long computation time. Results: The BCM elect the best candidates that give the lowest combinations to get the optimal solution. Conclusion/Recommendations: The BCM minimize the computation time and reduce the complexity where we can apply this method to different area of optimization problems.

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An Efficient Logarithmic Barrier Method without Line Search for Convex Quadratic Programming

Chaghoub

Benterki

2022

Numer. Analys. Appl.

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Optimization of a Quadratic Function under its Canonical Form

Cited by 7 publications

References 0 publications

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

The Best Candidates Method for Solving Optimization Problems

An Efficient Logarithmic Barrier Method without Line Search for Convex Quadratic Programming

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