Klatt, M Munk, A Zemel, Y

Abstract
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding random linear program, we characterize under general assumptions the random fluctuations of the empirical optimal solutions around their population quantities after standardization by a dist...

Adami, R Boni, F Carlone, R Tentarelli, L

We investigate the ground states for the focusing, subcritical nonlinear Schrodinger equation with a point defect in dimension two, defined as the minimizers of the energy functional at fixed mass. We prove that ground states exist for every positive mass and show a logarithmic singularity at the defect. Moreover, up to a multiplication by a consta...

Fajardo, Maria Dolores Grad, Sorin-Mihai Vidal, Jose

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for c...

Korn, Peter
Published in
Journal of Nonlinear Science

For the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose no...

Zhong, Li-nan Jin, Yuan-feng
Published in
Acta Mathematicae Applicatae Sinica, English Series

This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints, denoted by (MMOP). More precisely, we first establish necessary conditions for optimal solutions to the problem (MMOP) by means of employing some advanced tools of variational analysis and generalized differentia...

Bouchitté, Guy Buttazzo, Giuseppe Champion, Thierry De Pascale, Luigi

We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which are sub-probabilities. We fi...

Colombo, Maria Di Marino, Simone
Published in
Annali di Matematica Pura ed Applicata (1923 -)

A standard question arising in optimal transport theory is whether the Monge problem and the Kantorovich relaxation have the same infimum; the positive answer means that we can pass to the relaxed problem without loss of information. In the classical case with two marginals, this happens when the cost is positive, continuous, and possibly infinite ...

Sonali, Sharma, Vikas Kailey, Navdeep
Published in
Acta Mathematica Scientia

In this paper, we emphasize on a nondifferentiable minimax fractional programming (NMFP) problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions. We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-ord...

Bredies, Kristian Carioni, Marcello
Published in
Calculus of Variations and Partial Differential Equations

In this paper we characterize sparse solutions for variational problems of the form minu∈Xϕ(u)+F(Au)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\min _{u\in X} \phi ...

Bouchitté, Guy Buttazzo, Giuseppe Champion, Thierry De Pascale, Luigi

We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which are sub-probabilities. We fi...