Several emerging applications, such as “Analytics of Things" and “Integrative Analytics" call for a fusion of statistical learning (SL) and stochastic optimization (SO). The Learning Enabled Optimization paradigm fuses ...

We propose a randomized gradient method for the handling of a convex function whose gradient computation is demanding. The method bears a resemblance to the stochastic approximation family. But in contrast to stochastic ...

We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyper-rectangle. ...

We present a decomposition method for the solution of stwo-stage stochastic programming problems. This is an approximate method that can handle problems with large number scenarios. At the beginning, only rough approximation ...

We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and ...

We propose a new framework for analyzing pricing theory for incomplete markets and contingent claims, using conjugate duality and optimization theory. Various statements in the literature of the fundamental theorem of asset ...

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost ...

Graver test sets for linear two-stage stochastic integer programs are studied. It is shown that test sets can be decomposed into finitely many building blocks whose number is independent of the number of scenarios of the ...

A new measure of risk is introduced for a sequence of random incomes adapted to some filtration. This measure is formulated as the optimal net present value of a stream of adaptively planned commitments for consumption. ...

We consider the problem of constructing mean-risk models which are consistent with the second degree stochastic dominance relation. By exploiting duality relations of convex analysis we develop the quantile model of ...