A Global Optimization Algorithm for Sum of Quadratic Ratios Problem with Coefficients

DOI

10.2991/iccasm.2012.333How to use a DOI?

Keywords

Quadratic Ratios Problem, quadratic constraints problem, linearization relaxation, branch and bound, global convergence

Abstract

In this paper a global optimization algorithm for solving sum of quadratic ratios problem with coefficients and nonconvex quadratic function constraints ( NSP ) is proposed. First, the problem NSP is converted into an equivalent sum of linear ratios problem with nonconvex quadratic constraints ( LSP ). Using linearization technique, the linearization relaxation of LSP is obtained. The whole problem is then solvable using the branch and bound method. In the algorithm, lower bounds are derived by solving a sequence of linear lower bounding functions for the objective function and the constraint functions of the problem NSP over the feasible region. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems. The numerical examples demonstrate that the proposed algorithm can easily be applied to solve problem NSP .

Copyright

© 2012, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Ying Ji
AU  - Yijun Li
PY  - 2012/08
DA  - 2012/08
TI  - A Global Optimization Algorithm for Sum of Quadratic Ratios Problem with Coefficients
BT  - Proceedings of the 2012 International Conference on Computer Application and System Modeling (ICCASM 2012)
PB  - Atlantis Press
SP  - 1305
EP  - 1307
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccasm.2012.333
DO  - 10.2991/iccasm.2012.333
ID  - Ji2012/08
ER  -