Online Non-parametric Estimation for Nonconvex Stochastic Programming

This paper presents a fusion of Stochastic Decomposition and the Majorization-Minimization algorithm (SD-MM) to solve a class of non-convex stochastic programs. The objective function is an expectation of a smooth concave function and a second-stage linear recourse function, which is common in stochastic programming (SP). This extension not only allows new stochastic difference-of-convex (dc) functions … Read more

A Regularized Smoothing Method for Fully Parameterized Convex Problems with Applications to Convex and Nonconvex Two-Stage Stochastic Programming

We present an approach to regularize and approximate solution mappings of parametric convex optimization problems that combines interior penalty (log-barrier) solutions with Tikhonov regularization. Because the regularized mappings are single-valued and smooth under reasonable conditions, they can be used to build a computationally practical smoothing for the associated optimal value function. The value function in … Read more