Abstract:

The purpose of the talk is to discuss the solvability of nonlinear inclusions in Absolute Neighborhood Retracts of normed spaces. The set-valued maps involved are subject to tangency conditions expressed in terms of normal and tangent cones suitable for such domains. Special attention is given to ANR's with Lipschitzian behavior for which tangency is expressed in terms of Clake's cones. Applications to optimization will be discussed if time permits.