Related papers: The regularity of some vector-valued variational i…
A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.
We establish partial regularity for vector-valued solutions to inhomogeneous elliptic systems in divergence form where the coefficients are possibly discontinuous with respect to $x$. More precisely, we assume a VMO-condition with respect…
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…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
Gradient schemes is a framework which enables the unified convergence analysis of many different methods -- such as finite elements (conforming, non-conforming and mixed) and finite volumes methods -- for $2^{\rm nd}$ order diffusion…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
In this paper we prove Holder regularity of the gradient for solutions of Dirichlet problem associate to degenerate elliptic equations, extending the recent result of Imbert and Silvestre. Indeed we obtain regularity up to the boundary and…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincar\'e inequalities. The key point is the study of an optimal weighted Wirtinger inequality.
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…
In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…