In this research, we study the applicability of object-oriented modeling techniques to stochastic optimization. We propose a methodology that uses the UML to model stochastic optimization problems.

We give a novel algorithm for stochastic strongly-convex optimization in the gradient oracle model which returns an O( 1 T )-approximate solution after T gradient updates. This rate of convergence is optimal in the gradient oracle model. This improves upon the previously known best rate of O( log(T ) T ), which was obtained by applying an online strongly-convex optimization algorithm with regre...

We give novel algorithms for stochastic strongly-convex optimization in the gradient oracle model which return a O( 1 T )-approximate solution after T iterations. The first algorithm is deterministic, and achieves this rate via gradient updates and historical averaging. The second algorithm is randomized, and is based on pure gradient steps with a random step size. This rate of convergence is o...

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic or<b...