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APPROCHES DE POINTS INTERIEURS ET DE LA PROGRAMMATION DC EN OPTIMISATION NON CONVEXE. CODES ET SIMULATIONS NUMERIQUES INDUSTRIELLES

Abstract : This Ph.D Thesis is mainly devoted to the combination of DC Programming techniques and the Interior Point programming approaches to deal with large scale nonconvex programs.
After a brief review of the general DC theory and algorithms, the interior point scheme is presented, the quasidefinite matrices class and its essential properties are reminded.
In the second chapter we introduce a new algorithm for nonlinear problems.The algorithm is based on Chen-Harker-Kanzow-Smale regularization technique and filter approach. In the third chapter we present our main contribution, a new primal-dual interior point algorithm for solving nonconvex programming problem. The new algorithm IPDCA, follows the DCA scheme to handle nonconvexity.
The fourth chapter is devoted to the integration of IPDCA in a B&B to globally solve nonconvex quadratic programming problems.
In the fifth chapter we integrate IPDCA in a B&B to globally solve a 0-1 quadratic programming problems.
In the sixth chapter we integrate DCA in a B&B procedure in which the lower bound is computed using monotonic optimization introduced by H. Tuy.
In the seventh chapter we proposed a restarting procedure for DCA based on global optimality conditions for convex quadratic maximization problems.
In the eighth chapter the two algorithms developed in chapter two and in chapter three are applied to solve a large scale structural mechanics problem. In the last chapter we use IPDCA for a machine learning with non positive kernels. The problem is a large scale nonconvex quadratic programming problem with a dense hessian matrix.
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https://tel.archives-ouvertes.fr/tel-00008475
Contributor : François Akoa <>
Submitted on : Sunday, February 13, 2005 - 2:28:24 AM
Last modification on : Tuesday, February 5, 2019 - 11:24:15 AM
Long-term archiving on: : Friday, September 14, 2012 - 11:10:31 AM

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  • HAL Id : tel-00008475, version 1

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François Akoa. APPROCHES DE POINTS INTERIEURS ET DE LA PROGRAMMATION DC EN OPTIMISATION NON CONVEXE. CODES ET SIMULATIONS NUMERIQUES INDUSTRIELLES. Mathématiques [math]. INSA de Rouen, 2005. Français. ⟨tel-00008475⟩

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