TY - JOUR
T1 - Optimality conditions for 2-regular problems with nonsmooth objective functions
AU - Arutyunov, A. V.
AU - Izmailov, A. F.
AU - Shvartsman, I.
N1 - Funding Information:
The research of the first author was supported by the Russian Foundation for Basic Research Grants 12-01-00427 and 12-01-00506 . The second author was supported by the Russian Foundation for Basic Research Grant 12-01-33023 .
PY - 2013
Y1 - 2013
N2 - For equality-constrained optimization problems with locally Lipschitzian objective functions, we derive meaningful first-order necessary conditions for local optimality without assuming conventional regularity of constraints. In the case of a smooth objective function, theories of optimality conditions of this kind have been developed in the last three decades. This work extends these results to the nonsmooth case, employing the generalized differentiation concepts of modern nonsmooth analysis. As a by-product of this development, we establish the upper estimate of the Mordukhovich subdifferential of the lower directional derivative. Some applications of these results to the problem of minimization of the maximum function and to the constrained version of a Steiner-type problem are discussed.
AB - For equality-constrained optimization problems with locally Lipschitzian objective functions, we derive meaningful first-order necessary conditions for local optimality without assuming conventional regularity of constraints. In the case of a smooth objective function, theories of optimality conditions of this kind have been developed in the last three decades. This work extends these results to the nonsmooth case, employing the generalized differentiation concepts of modern nonsmooth analysis. As a by-product of this development, we establish the upper estimate of the Mordukhovich subdifferential of the lower directional derivative. Some applications of these results to the problem of minimization of the maximum function and to the constrained version of a Steiner-type problem are discussed.
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U2 - 10.1016/j.na.2013.05.021
DO - 10.1016/j.na.2013.05.021
M3 - Article
AN - SCOPUS:84879293459
SN - 0362-546X
VL - 90
SP - 37
EP - 45
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -