Abstract
This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.
Highlights
There are so many real life applications for the convex quadratic programming (QP) problem
In this paper we present a new heuristic to linearise the convex quadratic programming problem
We are unable to apply the simplex algorithm due to restricted base entry and this makes the simplex method approximately 8 times slower than its full speed compared to its unrestricted basis version
Summary
There are so many real life applications for the convex quadratic programming (QP) problem. Some of the methods for solving the convex quadratic problem are active set, interior point, branch and bound, gradient projection, and Lagrangian methods, see [4]-[9] for more information on these methods. In this paper we present a new heuristic to linearise the convex quadratic programming problem. (2015) A New Heuristic for the Convex Quadratic Programming Problem. Some computational experiments have been carried out and the objective of the computational experiments was to determine CPU times of the: 1) Proposed heuristic; 2) Regularised Active Set Method Mae and Saunders [10]; 3) Primal-Dual Interior Point Algorithm.
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