9 papers
On the Resolution of Stochastic MPECs over Networks: Distributed Implicit Zeroth-Order Gradient Tracking Methods
Mohammadjavad Ebrahimi, Uday V. Shanbhag, Farzad Yousefian
The mathematical program with equilibrium constraints (MPEC) is a powerful yet challenging class of constrained optimization problems, where the constraints are characterized by a…
Complexity Guarantees for Zeroth-order Methods via Exponentially-shifted Gaussian Smoothing: Mitigating Dimension-dependence and Incorporating Decision-dependence
Mingrui Wang, Prakash Chakraborty, Uday V. Shanbhag
In this paper, we consider two distinct challenges in the resolution of nonsmooth stochastic optimization. Of these, the first pertains to the pronounced dependence of dimension in…
Equilibrium Invariance, Proximality, and Surrogation: Moreau-Smoothed Best-Response Pathways in Stochastic Nonsmooth Games
Zhuoyu Xiao, Uday V. Shanbhag
Best-response (BR) schemes represent an important avenue for learning equilibria in noncooperative games. However, extant rate guarantees for BR schemes generally necessitate strin…
A Parameter-Free Stochastic LineseArch Method (SLAM) for Minimizing Expectation Residuals
Qi Wang, Uday V. Shanbhag, Yue Xie
Most existing rate and complexity guarantees for stochastic gradient methods in -smooth settings mandates that such sequences be non-adaptive, non-increasing, and upper bounded…
On the Sampling-based Computation of Nash Equilibria under Uncertainty via the Nikaido-Isoda Function
Luke Marrinan, Farzad Yousefian, Uday V. Shanbhag
We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be -Lipschitz continuous and convex given ri…
Zeroth-order Gradient and Quasi-Newton Methods for Nonsmooth Nonconvex Stochastic Optimization
Luke Marrinan, Uday V. Shanbhag, Farzad Yousefian
We consider the minimization of a Lipschitz continuous and expectation-valued function, denoted by and defined as $f(\mathbf{x}) \triangleq \mathbb{E}[\tilde{f}(\mathbf{x}, \ma…