2 research outputs found
Generalized Differentiation of Parameter-Dependent Sets and Mappings
The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper
Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC)
In this paper, we consider a multiobjective optimal control problem where the
preference relation in the objective space is defined in terms of a pointed
convex cone containing the origin, which defines generalized Pareto optimality.
For this problem, we introduce the set-valued return function V and provide a
unique characterization for V in terms of contingent derivative and
coderivative for set-valued maps, which extends two previously introduced
notions of generalized solution to the Hamilton-Jacobi equation for single
objective optimal control problems.Comment: 29 pages, submitted to SICO