Tuesday, 16:15 - 16:40 h, Room: H 2036

 

Jose Herskovits
A feasible direction interior point algorithm for nonlinear convex semidefinite programming

Coauthors: Miguel Aroztegui, Jean R. Roche

 

Abstract:
The present method employs basic ideas of FDIPA [1], the Feasible Direction Interior Point Algorithm for nonlinear optimization. It generates a descent sequence of points at the interior of the feasible set, defined by the semidefinite constraints. The algorithm performs Newton-like iterations to solve the first order Karush-Kuhn-Tucker optimality conditions. At each iteration, two linear systems with the same coefficient matrix must be solved. The first one generates a descent direction. In the second linear system, a precisely defined perturbation in the left hand side is done and, as a consequence, a descent feasible direction is obtained. An inexact line search is then performed to ensure that the new iterate is interior and the objective is lower. A proof of global convergence of is presented. Some numerical are described. We also present the results with structural topology optimization problems employing a mathematical model based on semidefinite programming. The results suggest efficiency and high robustness of the proposed method.



  1. Herskovits J. A Feasible Directions Interior Point Technique For Nonlinear Optimization. JOTA, v. 99, n. 1, p. 121-146, 1998.


 

Talk 3 of the invited session Tue.3.H 2036
"First-derivative and interior methods in convex optimization" [...]
Cluster 4
"Conic programming" [...]

 

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