A remark on problems with nonnegative variable in mathematical programming

• Autorzy: Galewski Marek
• Języki publikacji: EN

Abstrakty

EN

We provide sufficient conditions involving invexity to the nonlinear programming problem with nonnegative variable and both inequality and equality constriants. We also consider the Mond-Wiers duals to such a problem.

Słowa kluczowe

EN

invexity; mathematical programming; Karush-Kuhn Tucker conditions; nonnegative variable

PL

zmienne nieujemne; programowanie matematyczne; warunek Karush-Kuhn Tuckera

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 2002
• Tom: z. 26 [199]
• Strony: 67--76
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Galewski Marek

• Faculty of Mathematics, University of Łódź, Łódź, Poland

Bibliografia

• [1] T. Antczak, Generalized r-convexity in mathematical programming, preprint Faculty of Mathematics, Lodz University, 1998.
• [2] M. S. Bazaara, H. D. Sherali, C. M. Shetty, Nonlinear Programming. Theory and Applications, J. Wiley 1991.
• [3] A. Ben - Israel, B. Mond, What is Invexity, J. Austral. Math. Soc., Ser. B 28 (1986), 1-9.
• [4] M. Galewski, On same connection between invex and convex problems in nonlinear programming, Control 8 Cybernetics, vol. (30), no. 1, 2001, pp. 1-9.
• [5] M. A. Hanson, On Sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981) pp. 545-550.
• [6] M. A. Hanson, B. M o n d, Necessary and Sufficient Conditions in Constraint Optimization, in FSU Statistic Report M 683, Florida State University, Dept. of Statistics, Tallahassee Florida, USA, 1984, 51-58.
• [7] O. L. Mangasarian , Nonlinear Programming, McGraw-Hill, New-York, 1969.
• [8] D. H. Martin, The Essence of Invexity, J. Optim. Theory Appl. 47, pp. 65-76, 1985.
• [9] B. Mond, T. Weir, Concave Functions and Duality in T. Schaible "Concavity and Economics", 1986.
• [10] T. W. Reiland, Nonsmooth invexity, Bull. Austral. Math. Soc., Vol. 42 (1990) pp. 437-446.