Search Results - "Set-Valued and Variational Analysis"

A Three-Operator Splitting Scheme and its Optimization Applications by Davis, Damek, Yin, Wotao

“…Operator-splitting methods convert optimization and inclusion problems into fixed-point equations; when applied to convex optimization and monotone inclusion…”
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Deep Neural Network Structures Solving Variational Inequalities by Combettes, Patrick L., Pesquet, Jean-Christophe

“…Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on…”
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Some Results on Strongly Pseudomonotone Quasi-Variational Inequalities by Nguyen, Luong V., Qin, Xiaolong

“…In this paper, strongly pseudomonotone quasi-variational inequalities are investigated. We provide sufficient conditions for existence and uniqueness of…”
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Convergence of Constant Step Stochastic Gradient Descent for Non-Smooth Non-Convex Functions by Bianchi, Pascal, Hachem, Walid, Schechtman, Sholom

“…This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function, defined as the…”
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Continuous Newton-like Inertial Dynamics for Monotone Inclusions by Attouch, Hedy, László, Szilárd Csaba

“…In a Hilbert framework ℌ, we study the convergence properties of a Newton-like inertial dynamical system governed by a general maximally monotone operator A ℌ:…”
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Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces by Takahashi, Wataru, Xu, Hong-Kun, Yao, Jen-Chin

“…Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve…”
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A Reflected Forward-Backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators by Cevher, Volkan, Vũ, Bằng Công

“…In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak…”
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Perspective Functions: Properties, Constructions, and Examples by Combettes, Patrick L.

“…Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest…”
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Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems by Ye, Jane J., Yuan, Xiaoming, Zeng, Shangzhi, Zhang, Jin

“…We study linear convergence of some first-order methods such as the proximal gradient method (PGM), the proximal alternating linearized minimization (PALM)…”
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A Maximum Principle for the Controlled Sweeping Process by Arroud, Chems Eddine, Colombo, Giovanni

“…We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone,…”
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Bregman Forward-Backward Operator Splitting by Bùi, Minh N., Combettes, Patrick L.

“…We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach…”
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Calculus for Directional Limiting Normal Cones and Subdifferentials by Benko, Matúš, Gfrerer, Helmut, Outrata, Jiří V.

“…The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite…”
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On the Analysis of Variance-reduced and Randomized Projection Variants of Single Projection Schemes for Monotone Stochastic Variational Inequality Problems by Cui, Shisheng, Shanbhag, Uday V.

“…Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such…”
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Optimal Control Involving Sweeping Processes by de Pinho, M. Rosário, Ferreira, M. Margarida, Smirnov, Georgi

“…Author's personal copy We present existence of solution and necessary conditions for an optimal control problem with a particular case of sweeping processes…”
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Sufficient Conditions for Metric Subregularity of Constraint Systems with Applications to Disjunctive and Ortho-Disjunctive Programs by Benko, Matúš, Červinka, Michal, Hoheisel, Tim

“…This paper is devoted to the study of the metric subregularity constraint qualification for general optimization problems, with the emphasis on the nonconvex…”
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Mordukhovich Derivatives of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces by Li, Jinlu

“…In this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders…”
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Sensitivity Analysis in Parametric Convex Vector Optimization by An, Duong Thi Viet, Tung, Le Thanh

“…In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation,…”
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A Variational Approach to a Cumulative Distribution Function Estimation Problem Under Stochastic Ambiguity by Deride, Julio, Urrea, Fernanda, Royset, Johannes O.

“…We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set…”
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The Intrinsic Core and Minimal Faces of Convex Sets in General Vector Spaces by Millán, R. Díaz, Roshchina, Vera

“…Intrinsic core generalises the finite-dimensional notion of the relative interior to arbitrary (real) vector spaces. Our main goal is to provide a…”
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On New Generalized Differentials with Respect to a Set and Their Applications by Qin, Xiaolong, Duc Thinh, Vo, Yao, Jen-Chih

“…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…”
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