UNICITY RESULTS FOR GENERAL LINEAR SEMIINFINITE OPTIMIZATION PROBLEMSUSING A NEW CONCEPT OF ACTIVE CONSTRAINTS

We consider parametric semi-infinite optimization problems without the usual asssumptions on the continuity of the involved mappings and on the compactness of the index set counting the inequalities. We establi sh a characterization of those optimization problems which have a uniq ue or strongly unique solution and which are stable under small pertub ations. This result generalizes a well-known theorem of Nurnberger The crucial roles in our investigations are a new concept of active const raints, a generalized Slater's condition, and a Kuhn-Tucker-type theor em. Finally, we give some applications in vector optimization, for app roximation problems in normed spaces, and in the stability of the mini mal value.