Introduction to sensitivity and stability analysis in nonlinear programming, Volume 165 (Mathematics in Science and Engineering) - ISBN:0122544501

Introduction to sensitivity and stability analysis in nonlinear programming, Volume 165 (Mathematics in Science and Engineering)

Date: 21 June 2011, 01:35

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Mathematical programming sensitivity and stability results are now abundant and far-reaching, but they are scattered in the literature. This has seriously diluted the impact of these results and impaired their systematic implementation, a eficiency compounded by the relatively small effort that has been made to make these results intelligible and accessible to nonmathematicians. Our purpose with this volume is to initiate seriously the process of unification and explication and to communicate the practical applicability and usefulness of many of these results to practitioners.
It is now feasible to develop software that allows for the calculation of sensitivity and stability information whenever a solution to a nonlinear programming (NLP) problem is calculated. It seems clear that nonlinear programming will not be a widely used or practical decision-making technique without this capability. (Witness the routine use of post-optimality analysis in linear programming.) Further, sensitivity and stability calculations and solution algorithm calculations often involve similar data and the same manipulations, so it appears natural and efficient to calculate the former as a by-product of the latter. We strongly support this approach and illustrate it via the detailed calculation of sensitivity and stability information by a classical penalty function method. Similar exploitation is indicated for Newton and projected- and reduced-gradient methods and for augmented Lagrangian algorithms. It should be stressed, however, that the basic sensitivity and stability results are presented in terms of the given problem functions and independently of any algorithmic manipulations.

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