A new approach to the regularized decomposition (RD) algorithm for two stage stochastic problems is presented. The RD method combines the ideas of the Dantzig-Wolfe decomposition principle and modern nonsmooth optimization methods. A new subproblem solution method using the primal simplex...

We give a general description of a new advanced implementation of the simplex method for linear programming. The method ``decouples'' a notion of the simplex basic solution into two independent entities: a solution and a basis. This generalization makes it possible to incorporate new strategies...

This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaido-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to...

The problem of water quality management under uncertain emission levels, reaction rates and pollutant transport is considered. Various performance measures: reliability, resiliency and vulnerability are taken into account. A general methodology for finding a cost-effective water quality...

A general class of iterative methods for saddle point seeking is developed. The directions used are subgradients evaluated at perturbed points. Convergence of the methods is proved and alternative strategies for implementation are discussed. The procedure suggests scalable algorithms for solving...

The linear programming problem is shown to be equivalent to a game in which primal players minimize the augmented Lagrangian function for the primal problem and dual players maximize the augmented Lagrangian function for the dual problem. Based on that, a parallel solution method is developed in...