Yi Chu

A Computational Toolbox for Linear Optimization with Joint Affine Chance Constraints

Categories Constrained Nonlinear Optimization, Linear Programming, Optimization Software Benchmark Tags , , , ,

We present a Julia computational toolbox for linear optimization problems with joint affine chance constraints under elliptically symmetric uncertainty. The toolbox combines a spherical–radial oracle for estimating the joint probability and its gradient with three structured optimization methods: Proximal, Feasible, and Penalty. The oracle supports several elliptically symmetric distributions and is integrated with these methods … Read more

A Proximal Approach for Nonsmooth Composite-Constrained Optimization

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

We propose a proximal-type algorithm for nonsmooth and nonconvex optimization problems with composite constraints. The constraint is defined by the composition of a locally upper-\(C^2\) outer function with a locally Lipschitz continuous inner mapping. The method is based on an improvement function that balances objective decrease and constraint satisfaction, and on a surrogate model obtained … Read more

Primal-dual resampling for solution validation in convex stochastic programming

Categories Convex Optimization, Optimization in Data Science, Stochastic Programming Tags , ,

Suppose we wish to determine the quality of a candidate solution to a convex stochastic program in which the objective function is a statistical functional parameterized by the decision variable and known deterministic constraints may be present. Inspired by stopping criteria in primal-dual and interior-point methods, we develop cancellation theorems that characterize the convergence of … Read more