In this paper we study several classes of stochastic optimization algorithms enriched with
heavy ball momentum. Among the methods studied are: stochastic gradient descent …

An algorithm is proposed for solving stochastic and finite-sum minimization problems. Based
on a trust region methodology, the algorithm employs normalized steps, at least as long as …

Decision making under uncertainty has been studied extensively over the last 70 years, if
not earlier. In the field of optimization, models for two-stage, stochastic, linear programming …

This paper considers an N-player stochastic Nash game in which the i th player minimizes a
composite objective fi (x)+ ri (xi), where fi is expectation-valued and ri has an efficient prox …

The motivation for this paper stems from the desire to develop an adaptive sampling method
for solving constrained optimization problems, in which the objective function is stochastic …

Mathematical programs with equilibrium constraints (MPECs) represent a class of
hierarchical programs that allow for modeling problems in engineering, economics, finance …

Classical theory for quasi-Newton schemes has focused on smooth, deterministic,
unconstrained optimization, whereas recent forays into stochastic convex optimization have …

The distributed computation of equilibria and optima has seen growing interest in a broad
collection of networked problems. We consider the computation of Nash equilibria of convex …

We consider monotone inclusions defined on a Hilbert space where the operator is given by
the sum of a maximal monotone operator T and a single-valued monotone, Lipschitz …

We consider a class of noncooperative hierarchical N-player games where the i th player
solves a parametrized stochastic mathematical program with equilibrium constraints (MPEC) …