Star-shaped probability function approximation is suggested. Conditions of log-concavity and differentiability of approximation function are obtained. The method for constructing stochastic estimates of approximation ...
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The concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover, in particular, the optimality conditions for a multistage stochasticprogramming problem. One of the...
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The concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover, in particular, the optimality conditions for a multistage stochasticprogramming problem. One of the long-standing methods for solving such an optimization problem under convexity is the progressive hedging algorithm. That approach is demonstrated here to be applicable also to solving multistage stochastic variational inequality problems under monotonicity, thus increasing the range of applications for progressive hedging. stochastic complementarity problems as a special case are explored numerically in a linear two-stage formulation.
Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where "multipliers" in a very general sense need to...
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Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where "multipliers" in a very general sense need to be brought in. Their stochastic version relates to problems of stochasticprogramming and covers not only classical formats with inequality constraints but also composite models with nonsmooth objectives. The progressive hedging algorithm, as a means of solving stochastic programming problems, has however focused so far only on optimality conditions that correspond to variational inequalities in primal variables alone. Here that limitation is removed by appealing to a recent extension of progressive hedging to multistage stochastic variational inequalities in general.
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