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A feasible direction algorithm for general nonlinear semidefinite programming

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Date
2017
Dewey
Analyse
Sujet
Nonlinear optimization; Semidefinite programming; Feasible directions; Interior-point methods; Structural optimization
Journal issue
Structural and Multidisciplinary Optimization
Volume
55
Number
4
Publication date
2017
Article pages
1261-1279
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00158-016-1564-5
URI
https://basepub.dauphine.fr/handle/123456789/20885
Collections
  • CEREMADE : Publications
Metadata
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Author
Roche, Jean-Rodolphe
211251 Institut Élie Cartan de Lorraine [IECL]
Herskovits, José
83486 Otimização Multidisciplinar em Engenharia [OptimizE / COPPE-UFRJ]
Bazán, Elmer
83486 Otimização Multidisciplinar em Engenharia [OptimizE / COPPE-UFRJ]
Zuniga, Andrés
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper deals with nonlinear smooth optimization problems with equality and inequality constraints, as well as semidefinite constraints on nonlinear symmetric matrix-valued functions. A new semidefinite programming algorithm that takes advantage of the structure of the matrix constraints is presented. This one is relevant in applications where the 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 nonlinear smooth optimization, FDIPA. FDIPA_GSDP makes iterations in the primal and dual variables to solve the first order optimality conditions. Given an initial feasible point with respect to the inequality constraints, FDIPA_GSDP generates a feasible descent sequence, converging to a local solution of the problem. At each iteration a feasible descent direction is computed by merely solving two linear systems with the same matrix. A line search along this direction looks for a new feasible point with a lower objective. Global convergence to stationary points is proved. Some structural optimization test problems were solved very efficiently, without need of parameters tuning.

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