A Numerical Approach to Optimization w.r.t. Variable-Dependent Constraint-Indices

Summary

We discuss the minimization of a continuous function on a subset of ℝⁿ subject to a finite set of continuous constraints. At each point, a given set-valued map determines the subset of constraints considered at this point. After a brief discussion on the existence of solutions, the numerical treatment of the problem is considered. It is motivated why standard approaches generally fail. A method is proposed approximating the original problem by a standard one depending on a parameter. By choosing this parameter large enough, each solution to the approximating problem is a solution to the original one. In many applications, an upper bound for this parameter can be computed, thus yielding the equivalence of the original problem to a standard optimization problem. The proposed method is applied to the problem of optimally designing a loaded truss subject to local buckling conditions.