Related papers: Convex Analysis of Minimal Time and Signed Minimal…
This paper concerns the study of a broad class of minimal time functions corresponding to control problems with constant convex dynamics and closed target sets in arbitrary Banach spaces. In contrast to other publications, we do not impose…
In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time…
In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of research by providing new results on generalized…
The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally…
Finding the minimum and the minimizers of convex functions has been of primary concern in convex analysis since its conception. It is well-known that if a convex function has a minimum, then that minimum is global. The minimizers, however,…
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 prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex…
We study the time optimal control problem for differential inclusions with a general closed target. We first give the representation of the proximal horizontal subgradients of the minimum time function $\mathcal{T}$ and then, together with…
This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation…
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.
In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of local convexity condition that is suitable to describe the…