An Implementation of Newton-Like Methods on Nonlinearly Constrained Network<br/>

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An Implementation of Newton-Like Methods on Nonlinearly Constrained Network

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39235 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
In this thesis, arranged by [6], the multiplier method is used to solve the network problems with nonlinear constraints and the Newton-like methods are used for updating the required parameters. This method, recently proposed in the literature, is based on solving a sequence of nonlinear optimization subproblems, dependent on the main problem, such that sequence of solutions of these problems converge to the solution of the main problem. In fact, to obtain an acceptable approximation of the main solution, it is needed to solve just a finite number of nonlinear subproblems. The main idea of the multiplier methods is based on eliminating some constraints and adding a penalty term to the objective function of the problem for considering the effect of constraint eliminations such that the new problem has the better formulation for solution. In the end, the algorithms of this method are run over two particular problems in the Matlab7.1 software environment and the numerical results are given
Keywords:
Nonlinear Programming ; Multiplier Method ; Lagrangian Method ; Newton Method

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