zbMATH — the first resource for mathematics

Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms. (English) Zbl 0294.90078

90C30 Nonlinear programming
90C25 Convex programming
49K40 Sensitivity, stability, well-posedness
65K05 Numerical mathematical programming methods
PDF BibTeX Cite
Full Text: DOI
[1] R.L. Armacost and A.V. Fiacco, ”Computational experience in sensitivity analysis for nonlinear programming”,Mathematical Programming 6 (1974) 301–326. · Zbl 0284.90074
[2] C. Berge,Topological spaces (Macmillan, New York, 1963). · Zbl 0114.38602
[3] G.B. Dantzig, J. Folkman and N.Z. Shapiro, ”On the continuity of the minimum set of a continuous function”,Journal of Mathematical Analysis and Applications 17 (1967) 519–548. · Zbl 0153.49201
[4] R.H. Day,Recursive programming and production response (North-Holland, Amsterdam, 1963).
[5] R.H. Day and P. Kennedy, ”Recursive decision systems: an existence analysis”,Econometrica 38 (1970) 666–681. · Zbl 0228.62005
[6] J.P. Evans and F.J. Gould, ”Stability in nonlinear programming”,Operations Research 18 (1970) 107–118. · Zbl 0232.90057
[7] A.V. Fiacco, ”Sensitivity analysis for nonlinear programming using penalty methods”, Tech. Paper, Serial T-275; Institute for Management Science and Engineering, The George Washington University, Washington, D.C. (March 1973). · Zbl 0357.90064
[8] A.V. Fiacco and G.P. McCormick,Nonlinear programming: sequential unconstrained minimization techniques (Wiley, New York 1968). · Zbl 0193.18805
[9] L.V. Kantorovich and G.P. Akilov,Functional analysis in normed spaces (Macmillan, New York 1964). · Zbl 0127.06104
[10] E.S. Levitin and B.T. Polyak, ”Constrained minimization methods”,U.S.S.R. Computational Mathematics and Mathematical Physics 6 (5) (1966) 1–50. [Original in Russian:Žurnal Vyčislitel’noi Matematiki i Matematičeskoi Fiziki 6 (5) (1966) 787–823.]
[11] G.P. McCormick, ”Penalty function versus nonpenalty function methods for constrained nonlinear programming problems”,Mathematical Programming 1 (1971) 217–238. · Zbl 0242.90051
[12] R.R. Meyer, ”The solution of non-convex optimization problems by iterative convex programming”, Dissertation, University of Wisconsin, Madison, Wis. (1968).
[13] R.R. Meyer, ”The validity of a family of optimization methods”,SIAM Journal on Control 8 (1970) 41–54. · Zbl 0194.20501
[14] J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970). · Zbl 0241.65046
[15] S.M. Robinson, ”A quadratically-convergent algorithm for general nonlinear programming problems”,Mathematical Programming 3 (1972) 145–156. · Zbl 0264.90041
[16] S.M. Robinson and R.H. Day, ”A sufficient condition for continuity of optimal sets in mathematical programming”,Journal of Mathematical Analysis and Applications 45 (1974) 506–511. · Zbl 0291.90063
[17] J.B. Rosen, ”Iterative solution of nonlinear optimal control problems”,SIAM Journal on Control 4 (1966) 223–244. · Zbl 0229.49025
[18] J.B. Rosen and J. Kreuser, ”A gradient projection algorithm for nonlinear constraints”, in:Numerical methods for nonlinear optimization, Ed. F.A. Lootsma (Academic Press, New York, 1972) pp. 297–300. · Zbl 0267.90077
[19] R.B. Wilson, ”A simplicial algorithm for concave programming”, Dissertation, Graduate School of Business Administration, Harvard University, Cambridge, Mass. (1963).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.