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Sensitivity analysis for nonlinear programming using penalty methods.(English)Zbl 0357.90064


MSC:

90C30 Nonlinear programming
49K40 Sensitivity, stability, well-posedness
93B35 Sensitivity (robustness)

Cite

References:

[1]R.L. Armacost and A.V. Fiacco, ”Computational experience in sensitivity analysis for nonlinear programming”,Mathematical Programming 6 (3) (1974) 301–326. ·Zbl 0284.90074 ·doi:10.1007/BF01580247
[2]C. Berge,Topological spaces (The Macmillan Co., New York, 1963). ·Zbl 0114.38602
[3]J.H. Bigelow and N.Z. Shapiro, ”Implicit function theorems for mathematical programming and for systems of inequalities”,Mathematical Programming 6 (2) (1974) 141–156. ·Zbl 0293.90032 ·doi:10.1007/BF01580232
[4]S. Bochner and W.T. Martin,Several complex variables (Princeton University Press, Princeton, N.J., 1948). ·Zbl 0041.05205
[5]J. Bracken and G.P. McCormick,Selected applications of nonlinear programming (Wiley, New York, 1968).
[6]J.D. Buys, ”Dual algorithms for constrained optimization problems”, Ph.D. Thesis, University of Leyden, the Netherlands (1972).
[7]B. Causey, ”A method for sensitivity of a solution of a nonlinear program”, RAC manuscript (1971), unpublished. ·Zbl 0212.10301
[8]G.B. Dantzig, J. Folkman and N. Shapiro, ”On the continuity of the minimum set of a continuous function”,Journal of Mathematical Analysis and its Applications 17 (1967) 519–548. ·Zbl 0153.49201 ·doi:10.1016/0022-247X(67)90139-4
[9]J.P. Evans and F.J. Gould, ”Stability in nonlinear programming”,Operations Research 18 (1) (1970). ·Zbl 0232.90057
[10]A.V. Fiacco, ”Convergence properties of local solutions of sequences of mathematical programming problems in general spaces”,Journal of Optimization Theory and its Applications 13 (1) (1974). ·Zbl 0255.90047
[11]A.V. Fiacco and G.P. McCormick,Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York, 1968). ·Zbl 0193.18805
[12]R.L. Fox,Optimization methods for engineering design (Addison-Wesley, Reading, Mass., 1971). ·Zbl 0232.76058
[13]H.J. Greenberg and W.P. Pierskalla, ”Extensions of the Evans–Gould stability theorems for mathematical programs”,Operations Research 20 (1) (1972). ·Zbl 0244.90037
[14]M.R. Hestenes,Calculus of variations and optimal control theory (Wiley, New York, 1966).
[15]F.A. Lootsma (ed.),Numerical methods for non-linear optimization (Academic Press, London, 1972).
[16]R. Meyer, ”The validity of a family of optimization methods”,SIAM Journal on Control 3 (1) (1970). ·Zbl 0194.20501
[17]W.C. Mylander, ”Estimating the sensitivity of a solution of a nonlinear program”, RAC manuscript (1971), unplublished.
[18]W.C. Mylander and R.L. Armacost, ”A guide to a SUMT-Version 4 computer subroutine for implementing sensitivity analysis in nonlinear programming”, The George Washington University, Technical Paper Serial 287, Program in Logistics (1973).
[19]S.M. Robinson, ”Perturbed Kuhn–Tucker points and rates of convergence for a class of nonlinear-programming algorithms”,Mathematical Programming 7 (1) (1974). ·Zbl 0294.90078
[20]L.A. Schmit, ”A basis for assessing the state-of-the-art”, AGARDograph No. 149, NATO Advisory Group for Aerospace R&D, Neuilly-sur-Seine, France (1971). ·Zbl 0252.73046
[21]W.A. Thornton and L.A. Schmit, ”Structural synthesis of an ablating thermostructural panel”, Preprint No. 68-332, AIAA/ASME 9th Structures, structural dynamics and materials conference, Palm Springs, Calif. (1968).
[22]G. Zoutendijk, ”Non-linear programming: a numerical survey”,SIAM Journal on Control 4 (1) (1966). ·Zbl 0146.13303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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