In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point of view. We formulate this in a time consistent way and deri...

The short term cost optimal dispatch of electric power in a generation sys tem under uncertain electricity demand is considered The system comprises thermal and pumped storage hydro units An operation model is developed which represents a multistage mixed integer stochastic program and a conceptual solution method using La grangian relaxation is sketched For xed start up and shut down decisions...

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.

In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. F...

Multistage stochastic programming problems belong to optimization problems depending on a probability measure. Usually, the operator of mathematical expectation appears in an objective function and, moreover, constraints set can depend on the probability measure also. The multistage stochastic programming problems correspond to applications (with an unneglected random element) that can be reaso...

In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. particular distributionally robust risk averse approaches to programming, the involved concept time consistency. This is aimed at presenting a certain point view on optimization, rather than complete survey topic.

Mobile communication is nowadays taken for granted. Having started primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. Operators are facing the challenge to match the demand by continuously expanding and upgrading the network infrastructure. However, the evolution of the customer’s demand is uncertain....

In this paper we discuss statistical properties and rates of convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently the SDDP alg...

We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming...