an:00770138
Zbl 0834.90120
Kummer, Bernd
On solvability and regularity of a parametrized version of optimality conditions
EN
Z. Oper. Res. 41, No. 2, 215-230 (1995).
00026532
1995
j
90C30 90C31
optimality condition; Kojima's system; embedding; nonsmooth equation; solvability; inverse function; Lipschitz-continuity; regularization; linear homotopy
Summary: We investigate a linear homotopy \(F(\cdot, t)\) connecting an appropriate smooth equation \(G= 0\) with Kojima's (nonsmooth) system \(K= 0\) describing critical points (primal-dual) of a nonlinear optimization problem (NLP) in finite dimension.
For \(t= 0\), our system may be seen e.g. as a starting system for an embedding procedure to determine a critical point to NLP. For \(t\approx 1\), it may be regarded as a regularization of \(K\). Conditions for regularity (necessary and sufficient) and solvability (sufficient) are studied. Though, formally, they can be given in a unified way, we show that their meaning differs for \(t< 1\) and \(t= 1\). Particularly, no MFCQ- like condition must be imposed in order to ensure regularity for \(t< 1\).