Ariyawansa and Zhu have introduced a class of volumetric barrier decomposition algorithms [5] for solving two-stage stochastic semidefinite programs with recourse (SSDPs) [4]. In this paper we utilize their work for SSDPs to derive a class of volumetric barrier decomposition algorithms for solving two-stage stochastic quadratic programs with recourse and to establish polynomial complexity of ce...

Abstruct-The discrete wavelet decomposition of second-order harmonizable random processes is considered. The deterministic wavelet decomposition of a complex exponential is examined, where its pointwise and bounded convergence to the function is proved. This result is then used for establishing the stochastic wavelet decomposition of harmonizable processes. The similarities and differences betw...

In this paper, we extend a recently proposed scenario decomposition algorithm (Ahmed (2013)) for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the ...

Many modern computer and communication systems result in large, complex performance models. The compositional approach ooered by stochastic process algebra constructs a model from submodels which are smaller and more easily understood. This gives the model a clear component-based structure. In this paper we present cases when this structure may be used to inform the solution of the model, leadi...

In the last decade, multi-stage stochastic programs with recourse have been broadly used to model real-world applications. This paper reviews the main optimization methods that are used to solve multi-stage stochastic programs with recourse. In particular, this paper reviews four types of optimization approaches to solve multi-stage stochastic programs with recourse: direct methods, decompositi...

This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this context as the L-shaped method), then extends this t...

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...