Related papers: Weak sharp minima for interval-valued functions an…

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…

The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…

In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomology of M, and illustrate this with an example. We also…

In this paper, we perform sensitivity analysis for the maximal value function which is the optimal value function for a parametric maximization problem. Our aim is to study various subdifferentials for the maximal value function. We obtain…

We have witnessed remarkable progress in foundation models in vision tasks. Currently, several recent works have utilized the segmenting anything model (SAM) to boost the segmentation performance in medical images, where most of them focus…

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…

In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we…

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…

Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on…

We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…

Weak gravitational lensing provides a sensitive probe of cosmology by measuring the mass distribution and the geometry of the low redshift universe. We show how an all-sky weak lensing tomographic survey can jointly constrain different sets…

Let $\varrho\in C^{\infty} ({\Bbb R}^d\setminus\{0\})$ be a non-radial homogeneous distance function satisfying $\varrho(t\xi)=t\varrho(\xi)$. For $f\in\frak S ({\Bbb R}^{d+1})$ and $\delta>0$, we consider convolution operator ${\Cal…

We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…

This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…

This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth…

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…

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…

We consider a pentadiagonal matrix which will be described in the text. We demonstrate practical methods for obtaining weak coupling expressions for the lowest eigenvector in terms of the parameters in the matrix, v and w. It is found that…

We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their…

Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid…