An ε-lagrange multiplier rule for a mathematical programming problem on banach spaces

The aim of this paper is to extend the multiplier rule due to Clarke for a nondifferentiable mathematical programming problem on a Banach space to epsilon -minimal (suboptimal) solutions of the problem. This seems to be useful above all for problems which have no optimal solution. Special cases which are already known can be derived very easy from the general epsilon -Lagrange multiplier rule, for example a result due to Ekeland for C-1-problems. A saddle point version in the case of convex data and a simple example will be given.