Abstract
This paper presents a method for obtaining computable bounds for the error in an approximate Kuhn—Tucker point of a nonlinear program. Techniques of interval analysis are employed to compute the error bounds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Apostolatos et al., “The algorithmic language Triplex-ALGOL 60”,Numerische Mathematik 11 (1968) 175–180.
A.V. Fiacco and G.P. McCormick,Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York, 1968).
E.R. Hansen, “On solving systems of equations using interval arithmetic”,Mathematics of Computation 22 (1968) 374–384.
T.D. Ladner and J.M. Yohe, “An interval arithmetic package for the UNIVAC 1108”, Technical Summary Report No. 1055, Mathematics Research Center, University of Wisconsin, Madison, Wisc. (1970).
R.E. Moore,Interval analysis (Prentice-Hall, Englewood Cliffs, N.J., 1966).
K. Nickel, “On the Newton method in interval analysis”, Technical Summary Report No. 1136, Mathematics Research Center, University of Wisconsin, Madison, Wisc. (1971).
S.M. Robinson, “Perturbed Kuhn—Tucker points and rates of convergence for a class of nonlinear-programming algorithms”, Technical Summary Report No. 1298, Mathematics Research Center, University of Wisconsin, Madison, Wisc. (1972), to appear inMathematical Programming.
Author information
Authors and Affiliations
Additional information
Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.
Rights and permissions
About this article
Cite this article
Robinson, S.M. Computable error bounds for nonlinear programming. Mathematical Programming 5, 235–242 (1973). https://doi.org/10.1007/BF01580124
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01580124