This paper presents a stochastic operational optimization method for metallurgical blending processes by focusing on the uncertainty of composition of raw materials, where the stochastic optimization model is firstly formulated by explicitly incorporating uncertain parameters into the constraints as random variables. Then an efficient sampling technique is utilized to construct the expectation ...

Stochastic optimization problems pose unique challenges in how they are represented mathematically. These problems arise in a number of different communities, often in the context of problems that introduce specific computational characteristics. As a result, a number of contrasting notational styles have evolved, which complicate our ability to communicate research across communities. This is ...

We introduce and analyze stochastic optimization methods where the input to each gradient updateis perturbed by bounded noise. We show that this framework forms the basis of a unified approachto analyze asynchronous implementations of stochastic optimization algorithms. In this framework,asynchronous stochastic optimization algorithms can be thought of as serial methods operatin...