Geodesic
SECOND ORDER CONVERSE DUALITY FOR NONLINEAR PROGRAMMING
AHMAD , I. 1 ; AGARWAL, RAVI P.2
1 Department of Mathematics, Aligarh Muslim University, Aligarh- 202 002, India;Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia
2 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, USA;Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 4, p. 234-244.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Chandra and Abha [European J. Oper. Res. 122 (2000), 161-165] considered a nonlinear programming problem over cone constraints and presented the correct forms of its four types of duals formulated by Nanda and Das [European J. Oper. Res. 88 (1996) 572-577]. Yang et al. [Indian J. Pure Appl. Math. 35 (2004), 699-708] considered the same problem and discussed weak and strong duality for its four types of second order duals under the assumptions of generalized second order F-convexity. In this paper, we are intended to prove converse duality theorems for second order duals of Yang et al.
DOI : 10.22436/jnsa.003.04.01
Classification : 90C30, 90C46
Keywords: Nonlinear programming, second order duality, converse duality, cone constraints.

AHMAD , I.  1 ; AGARWAL, RAVI P. 2

1 Department of Mathematics, Aligarh Muslim University, Aligarh- 202 002, India;Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia
2 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, USA;Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia 
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AHMAD , I. ; AGARWAL, RAVI P. SECOND ORDER CONVERSE DUALITY FOR NONLINEAR PROGRAMMING. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 4, p. 234-244. doi : 10.22436/jnsa.003.04.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.04.01/

[1] Bazaraa, M. S.; Goode, J. J. On symmetric duality in nonlinear programming, Oper. Res., Volume 21 (1973), pp. 1-9

[2] Chandra, S.; Abha A note on pseudo-invexity and duality in nonlinear programming, European J. Oper. Res., Volume 122 (2000), pp. 161-165

[3] Das, L. N.; Nanda, S. Pseudo-invexity and duality in nonlinear programming, European J. Oper. Res., Volume 88 (1996), pp. 572-577

[4] Yang, X. M.; Yang, X. Q.; K. L. Teo; Hou, S. H. Second order duality for nonlinear programming , Indian J. Pure Appl. Math., Volume 35 (2004), pp. 699-708

[5] Yang, X. M.; Yang, X. Q.; Teo, K. L. Converse duality in nonlinear programming with cone constraints, European J. Oper. Res., Volume 170 (2006), pp. 350-354

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