Lower Studniarski derivative of the perturbation map in parametrized vector optimization

Stability Analysis for Higher-Order Adjacent Derivative in Parametrized Vector Optimization

Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives

We introduce lower and upper limits of vector-valued functions with respect to the usual positive cone in a finite-dimensional space. Using these concepts, we extend the definitions ofm-th order lower and upper directional derivatives introduced in Studniarski (1986) [1] to vector-valued functions, and prove some necessary and sufficient conditions for strict local Pareto minimizers of orderm. ...

Stability of Linear-Quadratic Minimization over Euclidean Balls

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...

Higher-order Contingent Derivative of Perturbation Maps in Multiobjective Optimization

In this paper, higher-order sensitivity analysis in multiobjective optimization problem is considered. First, relations between higher-order contingent derivative, or their minima, of a set-valued map and its profile map are investigated. Then, properties of higher-order contingent derivatives of the perturbation maps of a parameterized optimization problem are obtained.

Optimality for set-valued optimization in the sense of vector and set criteria

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.