NDLI: A feasible direction algorithm for general nonlinear semidefinite programming

Content Provider	Springer Nature Link
Author	Roche, Jean Rodolphe Herskovits, José Bazán, Elmer Zúñiga, Andrés
Copyright Year	2016
Abstract	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.
Starting Page	1261
Ending Page	1279
Page Count	19
File Format	PDF
ISSN	1615147X
Journal	Structural and Multidisciplinary Optimization
Volume Number	55
Issue Number	4
e-ISSN	16151488
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-08-26
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear optimization Semidefinite programming Feasible directions Interior-point methods Structural optimization Theoretical and Applied Mechanics Computational Mathematics and Numerical Analysis Engineering Design
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Computer Graphics and Computer-Aided Design Control and Systems Engineering Computer Science Applications Software

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