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Tight Ergodic Sublinear Convergence Rate of the Relaxed Proximal Point Algorithm for Monotone Variational Inequalities
This paper considers the relaxed proximal point algorithm for solving monotone variational inequality problems, and our main contribution is the...
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On the linear convergence rate of Riemannian proximal gradient method
Composite optimization problems on Riemannian manifolds arise in applications such as sparse principal component analysis and dictionary learning....
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Convergence Rate of Gradient-Concordant Methods for Smooth Unconstrained Optimization
The article discusses the class of gradient-concordant numerical methods for smooth unconstrained minimization where the descent direction is...
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Small order limit of fractional Dirichlet sublinear-type problems
We study the asymptotic behavior of solutions to various Dirichlet sublinear-type problems involving the fractional Laplacian when the fractional...
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On asymptotic convergence rate of random search
This paper presents general theoretical studies on asymptotic convergence rate (ACR) for finite dimensional optimization. Given the continuous...
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Geometry and convergence of natural policy gradient methods
We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular...
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A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses
This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal...
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Exact convergence rates of alternating projections for nontransversal intersections
We consider the convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear...
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Equivalent conditions of complete convergence and Marcinkiewicz–Zygmund-type strong law of large numbers for i.i.d. sequences under sub-linear expectations
Under suitable conditions, we study the equivalent conditions of complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers...
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Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization
In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex...
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Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps...
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Understanding the Convergence of the Preconditioned PDHG Method: A View of Indefinite Proximal ADMM
The primal-dual hybrid gradient (PDHG) algorithm is popular in solving min-max problems which are being widely used in a variety of areas. To improve...
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On Convergence Rates of Proximal Alternating Direction Method of Multipliers
In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first...
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On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces
In this paper, the convergence of the fundamental alternating minimization is established for non-smooth non-strongly convex optimization problems in...
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Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used...
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Convergence rate of block-coordinate maximization Burer–Monteiro method for solving large SDPs
Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group...
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Convergence Analysis under Consistent Error Bounds
We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This...
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Complete moment convergence for ND random variables under the sub-linear expectations
In this article, we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND) random variables under...
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Asymptotic linear convergence of fully-corrective generalized conditional gradient methods
We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and...
