Abstract
We investigate a linear homotopyF(·,t) connecting an appropriate smooth equationG=0 with Kojima's (nonsmooth) systemK=0 describing critical points (primal —dual) of a nonlinear optimization problem (NLP) in finite dimension.
Fort=0, our system may be seen e.g. as a starting system for an embedding procedure to determine a critical point to NLP. Fort≈1, it may be regarded as a regularization ofK.
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 fort < 1 andt=1. Particularily, no MFCQ-like condition must be imposed in order to ensure regularity fort < 1.
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Kummer, B. On solvability and regularity of a parametrized version of optimality conditions. ZOR - Mathematical Methods of Operations Research 41, 215–230 (1995). https://doi.org/10.1007/BF01432656
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DOI: https://doi.org/10.1007/BF01432656