NONLINEAR OPTIMIZATION - ON CONNECTED COMPONENTS OF LEVEL SETS

This paper is concerned with differentiable constrained optimization problems in finite dimensions. The constraint qualification used is of Mangasarian-Fromovitz type. This paper studies the connected component of the level set of the objective function containing a specific local minimizer, considering that component as a function of the objective level. Special attention is paid to compactness and continuity aspects, also in connection with the occurrence of stationary points. Moreover, a covering of such a compact connected component is presented with differentiable curves tending to the specific local minimizer along which the objective function monotonically decreases.