Combining DCA (DC Algorithms) and interior point techniques for large-scale nonconvex quadratic programming

Authors:
T. Pham Dinh;H. A. Le Thi;F. Akoa
Affiliations:
Laboratory of Modelling, Optimization and Operations Research (LMI) National Institute for Applied Sciences, Rouen, Cedex, France;Laboratory of Theoretical and Applied Computer Science (LITA) UFR MIM, University of Paul Verlaine, Metz, Cedex, France;Laboratory of Modelling, Optimization and Operations Research (LMI) National Institute for Applied Sciences, Rouen, Cedex, France
Venue:
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Year:
2008

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Abstract

In this paper, we provide a new regularization technique based on DC programming and DC Algorithms to handle indefinite Hessians in a primal-dual interior point context for nonconvex quadratic programming problems. The new regularization leads automatically to a strongly factorizable quasidefinite matrix in the Newton system. Numerical results show the robustness and the efficiency of our approach compared with LOQO. Moreover, in our computational testing, our method always provided globally optimal solutions to those nonconvex quadratic programs that arise from reformulations of linear complementarity problems.