Related papers: Non-subdifferentiability optimality and mean value…

This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…

We investigate the uniform convergence of subdifferential mappings from empirical risk to population risk in nonsmooth, nonconvex stochastic optimization. This question is key to understanding how empirical stationary points approximate…

Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…

Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…

The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the…

A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…

A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…

We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…

In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…

This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…

We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance…

This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by…