Optimality conditions with Lagrange multipliers for inequality constrained quasidifferentiable optimization. (English) Zbl 1029.90077

Gao, Yan

Demyanov, V. (ed.) et al., Quasidifferentiability and related topics. Dedicated to Prof. Franco Giannessi on his 65th birthday and to Prof. Diethard Pallaschke on his 60th birthday. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 43, 151-162 (2000).

It is shown in this paper that for a constrained optimization problem with quasidifferentiable and locally Lipschitz data, a Fritz John condition expressed in terms of Demyanov-Rubinov’s quasidifferential implies the same condition expressed in terms of Clarke’s subdifferential, and that for this problem a necessary optimality condition can be obtained by combining the above two differentials. Some sufficient conditions are also given via quasidifferential.
For the entire collection see [Zbl 0949.00047].

Reviewer: Dinh The Luc (Avignon)

MSC:

90C46	Optimality conditions and duality in mathematical programming
49K27	Optimality conditions for problems in abstract spaces
90C30	Nonlinear programming

Keywords:

nonsmooth optimization; constrained optimization; Clarke’s subdifferential