By A.G. Buckley, J-.L. Goffin
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Extra resources for Algorithms for Constrained Minimization of Smooth Nonlinear Functions (Mathematical programming study)
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 ; 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' : 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).
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