Related papers: Stochastic Primal-Dual Coordinate Method for Nonli…
In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…
We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical…
We formulate pure characteristics demand models under uncertainties of probability distributions as distributionally robust mathematical programs with stochastic complementarity constraints (DRMP-SCC). For any fixed first-stage variable and…
We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual…
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) for nonseparable minimization models with quadratic coupling terms. The novel convergence…
This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information…
Distance measurements demonstrate distinctive scalability when used for relative state estimation in large-scale multi-robot systems. Despite the attractiveness of distance measurements, multi-robot relative state estimation based on…
To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…
As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…
In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…