Nonlinear optimization in IRN
Semi-infinite optimization structure and stability of the feasible set
Journal of Optimization Theory and Applications
On Generic One-Parametric Semi-Infinite Optimization
SIAM Journal on Optimization
On the equivalence of parametric contexts for linear inequality systems
Journal of Computational and Applied Mathematics
Generalized Semi-Infinite Programming: on generic local minimizers
Journal of Global Optimization
Generalized Semi-Infinite Programming: The Nonsmooth Symmetric Reduction Ansatz
SIAM Journal on Optimization
Hi-index | 0.00 |
Feasible sets in semi-infinite optimization are basically defined by means of infinitely many inequality constraints. We consider one-parameter families of such sets. In particular, all defin-ing functions - including those defining the index set of the inequality constraints - will depend on a parameter. We note that a semi-infinite problem is a two-level problem in the sense that a point is feasible if and only if all global minimizers of a corresponding marginal function are nonnegative. For a quite natural class of mappings we characterize changes in the global topological structure of the corresponding feasible set as the parameter varies. As long as the index set (-mapping) of the inequality constraints is lower semicontinuous, all changes in topology are those which generically appear in one-parameter sets defined by finitely many constraints. In the case, however, that some component of the mentioned index set is born (or vanishes), the topological change is of global nature and is not controllable. In fact, the change might be as drastic as that when adding or deleting an (arbitrary) inequality constraint.