A feasible direction interior point algorithm for general nonlinear semidefinite programming
Résumé
This paper deals with nonlinear smooth optimization problems with equality and inequality constraints , as well as semidefinite constraints on symmetric matrix-valued functions. We present first a new semidefinite programming algorithm that takes advantage of the structure of the matrix constraints. This is relevant in applications where these matrices have a favorable structure, as in the case when finite element models are employed. FDIPA GSDP is then obtained by integration of this new method with the well known Feasible Direction Interior Point Algorithm for nonlin-ear smooth optimization, FDIPA. FDIPA GSDP makes iteration in the primal and dual variables to solve the first order optimality conditions. Given an initial interior point, FDIPA GSDP generates a descent interior sequence, converging to a local solution of the problem. At each iteration a feasible descent direction is defined. A line search along this direction looks for a new interior point with s lower objective. Global convergence to stationary points is proved. Some structural optimization test problems were solved very efficiently, without need of parameters tuning.
Origine : Fichiers produits par l'(les) auteur(s)
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