On Solving Stochastic Nonlinear Minimax Formulations

Event Sponsor: 
Mathematics and Computer Science Division LANS Seminar
Start Date: 
Apr 5 2017 - 3:00pm
Building/Room: 
Building 240/Room 1404-1405
Location: 
Argonne National Laboratory
Speaker(s): 
Soumyadip Ghosh
Speaker(s) Title: 
IBM
Host: 
Stefan Wild

We study stochastic minimax formulations that are not in the standard convex-concave format. Our motivation is a specific energy systems application that optimizes total profit by jointly maximizing the non-concave revenue obtained from power export while minimizing the cost of power generation, where yield from renewable generation and/or power grid reliability is subject to uncertainty. The standard technique of sample average approximation (SAA) of a Lagrangian reformulation does not work well in this case. We propose a stochastic first-order (gradient following) recursion procedure to solve the outer (minimization) problem that uses an SAA version of the inner (maximization) problem and parametric programming to estimate the gradient required. The method lends itself naturally to parallelization in implementation. We provide conditions under which the procedure converges. The method can also be computationally efficient (in a certain precise sense) if the rate at which sampling is done in the gradient estimation step is carefully controlled. We specify the regimes when the fastest possible convergence rates are achieved.

Miscellaneous Information: 

Coffee and goodies will be served.

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