In this thesis, a Benders decomposition algorithm is designed and implemented to solve both deterministic and stochastic pooling problems to global optimality. Convergence of the algorithm to a global optimum is proved and then it is implemented both in GAMS and C++ to get the best performance. A series of example problems are solved, both with the proposed Benders decomposition algorithm and c...

Realistic models of computer and communication systems result in large, complex performance models. Compositionality, offered by stochastic process algebra constructs a model from submodels which are smaller and more tractable. We present a technique to exploit this structure in order to enhance the solution of the model by decomposition of the underlying Markov process. The decomposition under...

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay ...

A dimensional decomposition method is presented for calculating the probabilistic characteristics of complex-valued eigenvalues and eigenvectors of linear, stochastic, dynamic systems. The method involves a function decomposition allowing lower-dimensional approximations of eigensolutions, Lagrange interpolation of lower-dimensional component functions, and Monte Carlo simulation. Compared with...

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates how it may be applied to any stochastic integer program with continuous recourse. Such programs are used to model many practical applications such as the one considered in this paper, network design...

In-house production or outsourcing are important strategic decisions for planning production and capacity in business organizations. Outsourcing to overseas suppliers is often associated with risk with respect to the quality of the products. Hence, we developed a multi-stage stochastic programming model that takes into account the uncertainty involved in the production of the quality of outsour...

This paper presents novel algorithms for nding the singular value decomposition (SVD) of a general covariance matrix by stochastic approximation. General in the sense that also non-square, between sets, covariance matrices are dealt with. For one of the algorithms, convergence is shown using results from stochastic approximation theory. Proofs of this sort, establishing both the point of equili...

We propose a scenario decomposition algorithm for stochastic 0-1 programs. The algorithm recovers an optimal solution by iteratively exploring and cutting-off candidate solutions obtained from solving scenario subproblems. The scheme is applicable to quite general problem structures and can be implemented in a distributed framework. Illustrative computational results on standard two-stage stoch...

The decomposition of a binary morphological structuring element is a well-known problem that has often been addresses in the literature. This work present a new approach based on an Evolution Program: using an iterative stochastic technique,it allows to determinethe optimal decomposition of an arbitrarily shaped binary morphological structuring element into the shortest chain of elementary fact...

In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.