Nonlinear Optimization: On Connected Components of Level Sets
Hubertus Th. Jongen, Jan Rueckmann · SIAM Journal on Control and Optimization · 1993
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.