The multiparametric 0-1-Integer Programming (0-1-IP)problem relative to the objective function is a family of 0-1-IP problemswhich are relatedby havingidentical constraint matrix and right-hand-sidevector. In this paper we present an algorithm to perform a completemultiparametric analysis relative to a generalized min max objectivefunction such that the min sum and min max are particular cases.

The multiparametric min max 0-1-Integer Programming (0-1-IP) problem relative to the objective function is a family of min max 0-1-IP problems which are related by having identical constraint matrix and right-hand-side vector. In this paper we present an algorithm to perform a completemultiparametric analysis relative to the objective function.

We consider optimal distributed and boundary control problemsfor semilinear parabolic equations, where pointwise constraints onthe control and pointwise mixed control-state constraints of bottlenecktype are given. Our main result states the existence of regularLagrange multipliers for the state-constraints. Under naturalassumptions, we are able to show the existence of bounded and measurableLagrange multipliers. The method is based on results from the theoryof continuous linear programming problems.