Optimal Control of Differential Inclusions

This paper is devoted to optimal control of dynamical systems governed by differential inclusions in both frameworks of Lipschitz continuous and discontinuous velocity mappings. The latter framework mostly concerns a new class of optimal control problems described by various versions of the so-called sweeping/Moreau processes that are very challenging mathematically and highly important in applications … Read more

Variational Analysis and Optimization of Sweeping Processes with Controlled Moving Sets

This paper briefly overviews some recent and very fresh results on a rather new class of dynamic optimization problems governed by the so-called sweeping (Moreau) processes with controlled moving sets. Uncontrolled sweeping processes have been known in dynamical systems and applications starting from 1970s while control problems for them have drawn attention of mathematicians, applied … Read more

Two-level value function approach to nonsmooth optimistic and pessimistic bilevel programs

The authors’ paper in Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analyzed in Ref. [4], for the case of optimistic bilevel programs. One of the basic assumptions in both of these … Read more

Variational Geometric Approach to Generalized Differential and Fenchel Conjugate Calculi in Convex Analysis

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their uni ed and simplified proofs based on the developed … Read more

Local monotonicity and full stability for parametric variational systems

The paper introduces and characterizes new notions of Lipschitzian and H\”olderian full stability of solutions to general parametric variational systems described via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, postulated certain quantitative properties of single-valued localizations of solution maps, are closely related to local strong maximal monotonicity of associated … Read more

Variational analysis and full stability of optimal solutions to constrained and minimax problems

The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with … Read more

Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of … Read more


This paper is devoted to the study of metric subregularity and strong subregularity of any positive order $q$ for set-valued mappings in finite and infinite dimensions. While these notions have been studied and applied earlier for $q=1$ and—to a much lesser extent—for $q\in(0,1)$, no results are available for the case $q>1$. We derive characterizations of … Read more

Minimal Points, Variational Principles, and Variable Preferences in Set Optimization

The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point … Read more

Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more