Xiaoyi Qu

A Stochastic Proximal-Gradient Method for Regularized Generally Constrained Continuous Optimization

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , ,

A stochastic proximal-gradient method is proposed and analyzed for solving regularized optimization problems subject to nonlinear equality constraints and nonnegativity bounds. The objective function’s values and gradients are available only through inexact stochastic oracles. The method decomposes each trial step into one component that reduces linearized infeasibility and a second component that seeks optimality while … Read more

A Proximal-Gradient Method for Solving Regularized Optimization Problems with General Constraints

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step acceptance or rejection. Under various assumptions, we establish a worst-case iteration complexity result, prove that limit points are first-order KKT points, … Read more

A Proximal-Gradient Method for Constrained Optimization

Categories Nonlinear Optimization, Optimization in Data Science Tags , , , , ,

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be viewed as an extension of the well-known proximal-gradient method that is applicable when constraints are not present. To account for nonlinear … Read more