Related papers: A minimax approach for inverse variational inequal…

In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…

This paper deals with inverse problems subject to imprecise or vague information of some involved data by means of interval-valued functions. To provide interval solutions to the inverse problems we have adopted a perturbed collage-based…

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…

We give a qualitative description of extremals for Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by extremals and the observation that extremals are optimal for a…

In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…

We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the…

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…