Related papers: Non-subdifferentiability optimality and mean value…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
We develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functionals, we introduce closed convex processes -- set-valued…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
Recently, several studies have claimed that using class-specific feature subsets provides certain advantages over using a single feature subset for representing the data for a classification problem. Unlike traditional feature selection…
We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…
This paper considers the minimization of a continuously differentiable function over a cardinality constraint. We focus on smooth and relatively smooth functions. These smoothness criteria result in new descent lemmas. Based on the new…
The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…
This paper deals with the problem of accurately determining guaranteed suboptimal values of an unknown cost function on the basis of noisy measurements. We consider a set-valued variant to regression where, instead of finding a best…
The Goldstein $\varepsilon$-subdifferential is a relaxed version of the Clarke subdifferential which has recently appeared in several algorithms for nonsmooth optimization. With it comes the notion of $(\varepsilon,\delta)$-critical points,…
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We…
This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
A hypodifferential is a compact family of affine mappings that defines a local max-type approximation of a nonsmooth convex function. We present a general theory of hypodifferentials of nonsmooth convex functions defined on a Banach space.…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…