Related papers: Monotone extensions into compact target sets in du…
In this paper we extend the classical Korovkin theorems to the framework of comonotone additive, sublinear and monotone operators. Based on the theory of Choquet capacities, several concrete examples illustrating our results are also…
Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from…
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized.…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…
In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and…
We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For…
The notion of Fej\'er monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of Fej\'er monotone sequences and we also provide…
This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality…
The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
We consider an abstract mixed variational problem governed by a nonlinear operator $A$ and a bifunctional $J$, in a real reflexive Banach space $X$. The operator $A$ is assumed to be continuous, Lipschitz continuous on each bounded subset…
We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
We study a canonical duality method to solve a mixed-integer nonconvex fourth-order polynomial minimization problem with fixed cost terms. This constrained nonconvex problem can be transformed into a continuous concave maximization dual…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…
We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…
We apply a modern axiomatic system of nonstandard analysis in metric fixed point theory. In particular, we formulate a nonstandard iteration scheme for nonexpansive mappings and present a nonstandard approach to fixed-point problems in…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…