Related papers: Monotone extensions into compact target sets in du…

In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order…

In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a…

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…

This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior…

In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…

In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization…

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…

We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…

The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…

Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving…

This paper considers endogenous selection models, in particular nonparametric ones. Estimating the unconditional law of the outcomes is possible when one uses instrumental variables. Using a selection equation which is additively separable…

Solutions of a variational inequality are found by giving conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to its natural map. One of these conditions is the isotonicity of the projection…

In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions.…

In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…

In this article, we examine two double-phase variable exponent problems, each formulated within a distinct framework. The first problem is non-variational, as the nonlinear term may depend on the gradient of the solution. The first main…

Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…