Optimization of multistage systems with nondifferentiable objective functions.
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PublisherThe University of Arizona.
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AbstractThis dissertation is aimed at a class of convex dynamic optimization problems in which the transition functions are twice continuously differentiable and the stagewise objective functions are convex, although not necessarily differentiable. Two basic descent algorithms which use sequential and parallel coordinating techniques are developed. In both algorithms the nondifferentiability of the objective function is accounted for by using subgradient information. The objective of the subproblems generated consists of successive piecewise linear approximations of the stagewise objective function and the value function. In the parallel algorithm, an incentive coordination method is used to coordinate the subproblems. We provide proofs of convergence for these algorithms. Two variations, namely, subgradient selection and subgradient aggregation, of the basic algorithms are also discussed. In practice while subgradient selection seems to perform well, computational results with subgradient aggregation are rather disappointing. Computational results of the basic algorithms and variants based on subgradient selection are given. The effect of number of stages on performance of these algorithms is compared with a general nonlinear programming package (NPSOL).
Degree ProgramSystems and Industrial Engineering