The semismooth approach for semi-infinite programming under the Reduction Ansatz
Journal of Global Optimization
Smoothing by mollifiers. Part I: semi-infinite optimization
Journal of Global Optimization
Global solution of bilevel programs with a nonconvex inner program
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Towards global bilevel dynamic optimization
Journal of Global Optimization
Global solution of nonlinear mixed-integer bilevel programs
Journal of Global Optimization
Computational Optimization and Applications
A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
Computational Optimization and Applications
Hi-index | 0.00 |
We present a new numerical solution method for semi-infinite optimization problems. Its main idea is to adaptively construct convex relaxations of the lower level problem, replace the relaxed lower level problems equivalently by their Karush-Kuhn-Tucker conditions, and solve the resulting mathematical programs with complementarity constraints. This approximation produces feasible iterates for the original problem. The convex relaxations are constructed with ideas from the $\alpha$BB method of global optimization. The necessary upper bounds for second derivatives of functions on box domains can be determined using the techniques of interval arithmetic, where our algorithm already works if only one such bound is available for the problem. We show convergence of stationary points of the approximating problems to a stationary point of the original semi-infinite problem within arbitrarily given tolerances. Numerical examples from Chebyshev approximation and design centering illustrate the performance of the method.