We use a decomposition approach to solve three types of realistic problems: blockangular linear programs arising in energy planning, Markov decision problems arising in production planning and multicommodity network problems arising in capacity planning for survivable telecommunication networks. Decomposition is an algorithmic device that breaks down computations into several independent subproblems. It is thus ideally suited to parallel implementation. To achieve robustness and greater reliability in the performance of the decomposition algorithm, we use the Analytic Center Cutting Plane Method (accpm) to handle the master program. We run the algorithm on two different parallel computing platforms: a network of PC's running under Linux and a genuine parallel machine, the IBM SP2. The approach is well adapted for this coarse grain parallelism and the results display good speed-up's for the classes of problems we have treated. Keywords Decomposition, Parallel computation, Analytic cent...

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report here on a deterministic equivalent linear programming model of 1,111,112 constraints and 2,555,556 variables generated by GAMS. It is solved by an interior point based decomposition method in less than 3 hours on a cluster of 10 Linux PC's. Key words. Algebraic modeling language, distributed systems, financial planning, large scale optimization, structure exploiting solver. 1 Introduction The curse of dimensionality is a major problem in optimization. To depict real life situations with greater accuracy, optimization models tend to be larger and larger, a trend that is probably encouraged by the rapid development of cheap and powerful computers. Unfortunately, hardware improvements This research was supported by the Fonds National de la Recherche Scientifique Suisse, grants #12-4250...

INTRODUCTION, APPLICATIONS AND ALGORITHMS, Nondifferentiable Optimization Introduction. Nondifferentiable, also known as nonsmooth, optimization (NDO) is concerned with problems where the smoothness assumption on the functions involved is relaxed. Nondifferentiability means that the gradient does not exist, implying that the function may have kinks or corner points. Consequently, the function cannot be approximated locally by a tangent hyperplane, or by a quadratic approximation. In NDO, the smoothness assumption is usually replaced by weaker ones, which at least guarantee the existence of directional derivatives. NDO problems arise in a variety of contexts, and methods designed for smooth optimization may fail to solve them. This justifies developing a specialized theory and methods that are the object of this short introduction. In the sequel, we will often refer to convex NDO, a subclass of nondifferentiable optimization,

The aim of this tutorial is to help users to formulate and solve a large variety of problems through the analytic center cutting plane method. We first briefly review the class of problems that are solvable by accpm and sketch the principles that underlie accpm. We discuss the organization of accpm as a general cutting plane method, and present its three modules: the oracle, the coordinator and the query point generator. The main interface is between the oracle that is problem-dependent, and thus programmed by the user, and the last two modules whose internal functions are hidden in most part to the user. We finally present some examples of optimization problems that can be solved by accpm, directly or after some reformulation.

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