By A.G. Buckley, J-.L. Goffin

ISBN-10: 0444863907

ISBN-13: 9780444863904

**Read Online or Download Algorithms for Constrained Minimization of Smooth Nonlinear Functions (Mathematical programming study) PDF**

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**Extra resources for Algorithms for Constrained Minimization of Smooth Nonlinear Functions (Mathematical programming study)**

**Sample text**

Nevertheless the algorithm can be improved further; its structure is such that heuristic modifications can easily be made without destroying its properties of global and superlinear convergence; several such modifications are suggested. The algorithm is naturally more complex than that given [5]; nevertheless the extra complexity does not add a significant computational burden and appears necessary. 2. The algorithm Superlinear convergence is achieved by using a search direction which is obtained by solving a quadratic approximation to the original problem P.

Exact minimization was employed in the earlier papers; obviously approximate minimization is preferable if convergence is not thereby destroyed. A third, problem is the 'Maratos effect' [7]: the exact penalty function step length procedure can truncate the step length near a solution when a quadratic approximation is employed to determine the search direction, thus destroying superlinear convergence. Finally the approximation to the original problem may not have a solution and may yield discontinuous estimates of the multipliers (required for choosing the penalty parameter).

Bertsekas, "Multiplier methods: A survey", Automatica 12 (1976) 133-145. M. L. Mangasarian, "Superlinearly convergent quasi-Newton algorithms for nonlinearly constrained optimization problems", Mathematical Programming 11 (1976) 1-13. P. Han, "Superlinearly convergent variable metric algorithms for general nonlinear programming problems", Mathematical Programming I1 (1976)263-282. D. ,. R. M. , Nonlinear programming 3 (Academic Press, New York 1978) 27--63. A. Tapia, "Diagonalized multiplier methods and quasi-Newton methods for constrained optimization", Journal off Optimization Theory and Applications 22 (1977) 135-194.