Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory

Study of the Parallel Variable Distribution Algorithms for Solving Optimization Problems

Author XuFangFang
Tutor HeGuoPing
School Shandong University of Science and Technology
Course Applied Mathematics
Keywords PVD Algorithm "Forget-me-not" term SQP Type PVD Algorithm Maratos Effect Inexact PVD Algorithm Mix-integer Nonlinear Optimization Problem
CLC O224
Type Master's thesis
Year 2010
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Parallel Variable Distribution algorithm(PVD algorithm) is a kind of parallel algorithm in the whole structure. The main difference from other algorithms is its "forget-me-not" term. Each processor has the primary responsibility for updating its block of variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions, which enhances robustness and flexibility of the algorithm. This thesis explains the important meaning of PVD algorithm by "forget-me-not" term.In order to get close to the reality, we need to improve the basic framework of PVD algorithm. The thesis gives the improvement direction of PVD algorithm, and puts forward two new PVD algorithms. Firstly, my thesis improves the existing SQP type PVD algorithm, and gives a new FSQP type PVD algorithm, whose search direction is the combination of descent direction, feasible direction and second-order revised direction. This new algorithm is very effective in preventing the occurrence of maratos effect. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. Secondly, we give a new inexact PVD algorithm for general optimization problem and the justification of its global convergence. In the algorithm, we choose projected gradient residual function as PVD direction, and we replace the minimization problem with a kind of sufficient descent condition.This thesis makes use of PVD algorithm to solve mix-integer nonlinear optimization problem. Its constraints are divided into:separable constrains and global constraints, then we compromise the global constrains to target function using penalty function method. So the mix-integer nonlinear optimization problem becomes separable constrained optimization problem, which can be solved by PVD algorithm of separable constrained optimization problem.

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