Mingyi Hong

A unified convergence analysis of block successive minimization methods for nonsmooth optimization

The block coordinate descent (BCD) method is widely used for minimizing a continuous function

On the linear convergence of the alternating direction method of multipliers

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Joint Base Station Clustering and Beamformer Design for Partial Coordinated Transmission in Heterogeneous Networks

of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed. To ensure the convergence of the BCD method, the subproblem of each block variable needs to be solved to its unique global optimal. Unfortunately, this requirement is often too restrictive for many practical scenarios. In this paper, we study an alternative inexact BCD approach which updates the variable blocks by successively minimizing a sequence of approximations of

Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems

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Transmit Solutions for MIMO Wiretap Channels using Alternating Optimization

which are either locally tight upper bounds of

Multi-Agent Distributed Optimization via Inexact Consensus ADMM

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Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems

or strictly convex local approximations of

Base Station Activation and Linear Transceiver Design for Optimal Resource Management in Heterogeneous Networks

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A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing

. The main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods, especially for the cases where the objective functions are either nondifferentiable or nonconvex. Our results unify and extend the existing convergence results ...

Iteration complexity analysis of block coordinate descent methods

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks. Moreover, there has been no rate of convergence analysis for the ADMM without strong convexity in the objective function. In this paper we establish the global R-linear convergence of the ADMM for minimizing the sum of any number of convex separable functions, assuming that a certain error bound condition holds true and the dual stepsize is sufficiently small. Such an error bound condition is satisfied for example when the feasible set is a compact polyhedron and the objective function consists of a smooth strictly convex function composed with a linear mapping, and a nonsmooth