A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorithm and Applications to Contact Problems

Authors: Figueiredo, Isabel¹; Júdice, Joaquim²; Rosa, Silvério³

Source: Optimization and Engineering, Volume 6, Number 2, June 2005 , pp. 203-239(37)

Publisher: Springer

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Abstract:

We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.

Keywords: nonlinear programming; complementarity problems; contact problems; finite elements; structural optimization

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11081-005-6796-y

Affiliations: 1: Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal, Email: isabel.figueiredo@mat.uc.pt 2: Departamento de Matemática, Instituto de Telecomunicações, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal, Email: joaquim.judice@co.it.pt 3: Departamento de Matemática, Universidade da Beira Interior, 6201-001, Covilhã, Portugal, Email: rosa@noe.ubi.pt

Publication date: 2005-06-01