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.
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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.
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Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.
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Robinson, S.M. Computable error bounds for nonlinear programming. Mathematical Programming 5, 235–242 (1973). https://doi.org/10.1007/BF01580124
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DOI: https://doi.org/10.1007/BF01580124