Abstract
A class of methods for solving general nonlinear semi-infinite programming problems is considered which may be shown to converge superlinearly to a solution, if for this solution a sufficient second order optimality condition holds. An important feature of all these methods is that they are related to the treatment of a finite programming problem. In the last two sections generalizations of "approximation methods" from nonlinear programming to the semi-infinite case are considered.
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References
L. Cromme: Eine Klasse von Verfahren zur Ermittlung bester nicht-linearer Tschebyscheff Approximationen, Numer. Math., 25 (1976), 447–459.
A.V. Fiacco: Sensitivity analysis for nonlinear programming using penalty methods, Math. Programming, 10 (1976), 287–311.
A.V. Fiacco and G.P. McCormick: Nonlinear programming: Sequential unconstrained minimization techniques, Wiley, New York, 1968.
S.A. Gustafson and K.O. Kortanek: Numerical treatment of a class of semi-infinite programming problems, Nav. Res. Log. Quart., 20 (1973), 477–504.
R. Hettich: A Newton method for nonlinear Chebyshev approximation, In: Approximation Theory, Lect. Notes in Math, 556 (1976), R. Schaback, K. Scherer, eds., Springer, Berlin-Heidelberg-New York, 222–236.
R. Hettich: A comparison of some numerical methods for semi-infinite programming, this volume.
R. Hettich and H. Th. Jongen: Semi-infinite programming: conditions of optimality and applications, In: Optimization Techniques, Part 2, Lecture Notes in Contr. and Inform. Sciences, 7 (1978), J. Stoer, ed., Springer, Berlin-Heidelberg-New York, 1–11.
R. Hettich and H.Th. Jongen: On first and second order conditions for local optima for optimization problems in finite dimensions, In: Methods of Operations Res. XXIII, R. Henn et al., Verlag A. Hain, Meisenheim a. Glan, 1977, 82–97.
W. van Honstede: An approximation method for semi-infinite problems, this volume.
I.M. Orthega and W.C. Rheinholdt: Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970.
S.M. Robinson: Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms, Math. Programming, 7 (1974), 1–16.
R.B. Wilson: A simplicial algorithm for concave programming, Graduate School of Business Administration, Harvard University, Cambridge, Mass., 1963.
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© 1979 Springer-Verlag
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Hettich, R., van Honstede, W. (1979). On quadratically convergent methods for semi-infinite programming. In: Hettich, R. (eds) Semi-Infinite Programming. Lecture Notes in Control and Information Sciences, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0003886
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DOI: https://doi.org/10.1007/BFb0003886
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