In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track inner layer function values we … Read more
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer … Read more
We discuss a tightly feasible mixed-integer linear programs arising in the energy industry, for which branch-and-bound appears to be ineffective. We consider its hardness, measure the probability that randomly generated instances are feasible or almost feasible, and introduce heuristic solution methods based on relaxing different constraints of the problem. We show the computational efficiency of … Read more