A new comptutational method for constrained nonlinear programming Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/70795b977

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  • In this dissertation, a new computational method for equality constrained nonlinear programming is developed. Specifically, problems of minimizing a nonlinear objective function f(x) subject to constraints h(x) = 0, where f is a scalar valued, x is an n-vector and h is a m-vector with m < n is considered. The approach employed is based on the idea of seeking simultaneous satisfaction of the associated necessary conditions and the constraints. This is achieved by modifying the normal penalty method approximation to the Lagrange multipliers associated with the problem. As a result of this modification, the new method permits a solution of the constrained problem through a single minimization of an equivalent unconstrained problem, for almost any choice of the associated penalty parameter ρ *. To evaluate the effectiveness and efficiency of the new method, its performance is compared with that of Hestenes' Multiplier and Fletcher's Exact Penalty Methods in the computational solution of a number of nonlinear programming examples. An important computational advantage of the proposed method over the two aforementioned methods is that it does not require the computation of the critical value ρ* , of the parameter p and provides almost unlimited freedom in its choice. The new method is shown to have superior convergence properties.
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