Initially, second-order necessary and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem φ(x)→ min, x ∈ R, are given. These conditions work with arbitrary functions φ, but they show inconsistency with the classical derivatives. This is a base to pose the question, whether the formulated optimality conditions remain true when ...

We show that the stopping criteria used in many support vector machine (SVM) algorithms working on the dual can be interpreted as primal optimality bounds which in turn are known to be important for the statistical analysis of SVMs. To this end we revisit the duality theory underlying the derivation of the dual and show that in many interesting cases primal optimality bounds are the same as kno...

BACKGROUND Support Vector Machine has become one of the most popular machine learning tools used in virtual screening campaigns aimed at finding new drug candidates. Although it can be extremely effective in finding new potentially active compounds, its application requires the optimization of the hyperparameters with which the assessment is being run, particularly the C and [Formula: see text]...

Topology optimization problem, which involves many design variables, is commonly solved by finite element method, a method must recalculate structure-stiffness matrix each time of analysis. OC method is a good way to solve topology optimization problem, nevertheless, it can not solve multiobjective topology optimization problems. This paper introduces an effective solution to Multi-objective to...

In this note we consider some notions of well-posedness for scalar and vector variational inequalities and we recall their connections with optimization problems. Subsequently, we investigate similar connections between well-posedness of a vector optimization problem and a related variational inequality problem and we present a result obtained with scalar characterizations of vector optimality ...

The vector criterion and set criterion are two defining approaches of solutions for the set-valued optimization problems. In this paper, the optimality conditions of both criteria of solutions are established for the set-valued optimization problems. By using Studniarski derivatives, the necessary and sufficient optimality conditions are derived in the sense of vector and set optimization.

In the paper we discuss the concepts of weak sharp solutions to vector optimization problems. As an application we provide sufficient conditions for stability of solutions in perturbed vector optimization problems.

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.