相关论文: Best Proximity Points for Geraghty-Type Non-Self M…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed.…

Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…

In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Sensor networks play a critical role in many situational awareness applications. In this paper, we study the problem of determining sensor placements to balance coverage and connectivity objectives over a target region. Leveraging algebraic…

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…

The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area…

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…

Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…

We consider a registration-based approach for localizing sensor networks from range measurements. This is based on the assumption that one can find overlapping cliques spanning the network. That is, for each sensor, one can identify…

In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…

Learning robust feature matching between the template and search area is crucial for 3D Siamese tracking. The core of Siamese feature matching is how to assign high feature similarity on the corresponding points between the template and…

The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric…

This paper aims to integrate the concepts of $F$-contraction and $S^B$-contraction within the context of super metric spaces. Specifically, we introduce the concepts of $S^F$-contraction and Bianchini $S^F$-contraction. We demonstrate that…

This paper investigates asymptotic fixed point results for nonlinear contractions, with emphasis on Kirk-type theorems and their generalizations. A central difficulty in the literature has been the requirement that the mapping possesses a…

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…