Related papers: Partial Smoothness, Subdifferentials and Set-value…
Motivated by the optimality principles for non-subdifferentiable optimization problems, we introduce new relative subdifferentials and examine some properties for relatively lower semicontinuous functions including $\epsilon$-regular…
Fully-automatic execution is the ultimate goal for many Computer Vision applications. However, this objective is not always realistic in tasks associated with high failure costs, such as medical applications. For these tasks, semi-automatic…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Observational data are often accompanied by natural structural indices, such as time stamps or geographic locations, which are meaningful to prediction tasks but are often discarded. We leverage semantically meaningful indexing data while…
In this study, we explore the partial identification of nonseparable models with continuous endogenous and binary instrumental variables. We show that the structural function is partially identified when it is monotone or concave in the…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…
Most existing person re-identification algorithms either extract robust visual features or learn discriminative metrics for person images. However, the underlying manifold which those images reside on is rarely investigated. That raises a…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the existence (and weak continuity) of the spectral density in a functional setting.…
Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually…
A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…
$\mathcal C^2$-partial smoothness of functions has been an important subject of research in optimization, on both theoretical and algorithmic aspects, since it was first introduced by Lewis in 2002. Our work aims at providing a fresh…