Abstract In this paper, for a nonsmooth semi-infinite multiobjective programming with locally Lipschitz data, some weak and strong Karush-KuhnTucker type optimality conditions are derived. The necessary conditions are proposed under a constraint qualification, and the sufficient conditions are explored under assumption of generalized invexity. All results are expressed in terms of Clarke subdif...

The Hölder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Hölder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal...

We first consider subsmoothness for a function family and provide formulas of the subdifferential of the pointwsie supremum of a family of subsmooth functions. Next, we consider subsmooth infinite and semi-infinite optimization problems. In particular, we provide several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum for such optimization problems.

and Applied Analysis 3 Proof. Since f(x) defined in (2) belongs to the PDGstructured family and by Lemma 2.1 in [16] the Clarke subdifferential of F(x, ρ) at x can be formulated by ∂F (x, ρ) = ∂f (x) + ρ∂G (x) = ∂f (x) + ρ conv { ∇g j (x) | j ∈ J (x) ∪ {0}}

This paper focuses on second-order necessary optimality conditions for constrained optimization problems Banach spaces. For in the classical setting, where objective function is $$C^2$$ -smooth, we show that strengthened are valid if constraint set generalized polyhedral convex. a new just assumed to be $$C^1$$ -smooth and convex, establish sharp based Fréchet subdifferential of tangent set. Th...

We study the farthest point mapping in a p-normed space X in virtue of subdifferential of rx sup{{x − z p : z ∈ M}, where M is a weakly sequentially compact subset of X. We show that the set of all points in X which have farthest point in M contains a dense G δ subset of X.