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Symmetric dual nondifferentiable programs

Published online by Cambridge University Press:  17 April 2009

S. Chandra
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
I. Husain
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
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Abstract

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Symmetric and selfduality results are established for a general class of nonlinear programs which combine differentiable as well as non-differentiable cases appearing in the literature. Many well known results are deduced as special cases and certain natural extensions are discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Craven, B.D. and Mond, B., “Lagrangean conditions for quasi–differentiable optimization”, Survey of mathematical programming, Vol. 1, 177192 (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976. North-Holland, Amsterdam, 1979).Google Scholar
[2]Craven, B.D. and Mond, B., “Sufficient Fritz John optimality conditions for nondifferentiable convex programming”. J. Austral. Math. Soc. Ser. B 19 (19751976), 462468.CrossRefGoogle Scholar
[3]Dantzig, G.B., Eisenberg, E., and Cottle, R.W., “Symmetric dual non-linear programs”, Pacific J. Math. 15 1965, 809812.CrossRefGoogle Scholar
[4]Hanson, M.A., “Duality and self-duality in mathematical programming”, SIAM J. Appl. Math. 12 1964, 446449.CrossRefGoogle Scholar
[5]Mehndiratta, S.L., “General symmetric dual programs”, Oper. Res. 14 1966, 164172.CrossRefGoogle Scholar
[6]Mehndiratta, S.L., “Symmetric and self-duality in nonlinear programming”, Numer. Math. 10 1967, 103109.CrossRefGoogle Scholar
[7]Mond, Bertram, “A symmetric dual theorem for non-linear programs”, Quart. Appl. Math. 23 1965, 265269.CrossRefGoogle Scholar
[8]Mond, Bertram, “A class of nondifferentiable mathematical programming problems”, J. Math. Anal. Appl. 46 1974, 169174.CrossRefGoogle Scholar
[9]Mond, B., “Symmetric duality for nonlinear programming”, Opsearch 13 1976, 110.Google Scholar
[10]Mond, Bertram and Cottle, Richard W., “Self–duality in mathematical programming”, SIAM J. Appl. Math. 14 1966, 420423.CrossRefGoogle Scholar
[11]Mond, Bertram and Hanson, Morgan A., “Symmetric duality for variational problems”, J. Math. Anal. Appl. 23 1968, 161172.CrossRefGoogle Scholar
[12]Mond, Bertram and Schechter, Murray, “A programming problem with an L p norm in the objective function”, J. Austral. Math. Soc. Ser. B 19 (1975/1976), 332342.Google Scholar