prox mapping – Optimization Online

On the Convergence Properties of Non-Euclidean Extragradient Methods for Variational Inequalities with Generalized Monotone Operators

Published: 2012/04/17, Updated: 2013/11/11

Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization complexity, extragradient methods, monotone variational inequality, non-euclidean methods, prox mapping, pseudo-monotone variational inequality

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing an approximate strong solution of these problems, and demonstrate how their iteration complexities depend on the global Lipschitz or H\”{o}lder continuity properties for their operators … Read more

Validation Analysis of Robust Stochastic Approximation Method

Published: 2008/05/20, Updated: 2009/05/25

Guanghui Lan

Arkadi Nemirovski

Alexander Shapiro

Stochastic Programming asset allocation problem, conditional-value-at-risk, large deviations estimates, mirror descent algorithm, monte carlo sampling, optimality bounds, prox mapping, sample average approximation method, stochastic approximation, stochastic programming

The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing robust stochastic approximation (SA) type algorithms. To this end we show that while running a Robust Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective … Read more