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A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorit...
Figueiredo, Isabel N.; Júdice, Joaquim J.; Rosa, Silvério S.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 ...
On the solution of a finite element approximation of a linear obstacle plate pr...
Fernandes, Luís M.; Figueiredo, Isabel N.; Júdice, Joaquim J.In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate tha...
Complementarity and genetic algorithms for an optimization shell problem
Figueiredo, Isabel N.; Júdice, Joaquim J.; Oliveira, Pedro N.The application of complementarity and genetic algorithms to an optimization thin laminated shallow shell problem is discussed. The discrete form of the problem leads to a Mathematical Program with Equilibrium Constraints (MPEC) [1], whose constraint set consists of a variational inequality and a set of equality constraints. Furthermore the variables are discrete. Special instances of the general problem are co...
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