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Stochastic generalizations of the extragradient method are complicated by a key challenge: the scheme requires two projections on a convex set and two evaluations of the map for every major iteration. We consider two related avenues where every iteration requires a single projection: (i) A projected reflected gradient (PRG) method requiring a single evaluation of the map and a single projection; and...
We consider a misspecified optimization problem that requires minimizing of a convex function f (x;θ*) in x over a constraint set represented by h(x;θ) ≤ 0 where θ* is an unknown (or misspecified) vector of parameters. Suppose θ* is learnt by a distinct process that generates a sequence of estimators θk, each of which is an increasingly accurate approximation of θ*. We develop a first-order augmented...
With increasing proportion of wind power, an important concern is that of maintaining the reliability of the electric grid in the face of higher supply-side volatility. In this paper, we examine the role of risk-based penalties in developing alternate designs in which firms combine energy bids associated with uncertain real-time availability with stable reserves bids. Such a study is carried out in...
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