Generalized (?,?)-convexity in nonsmooth vector optimization over cones

KAPOOR, Malti; SHARMA, Sunila; SUNEJA, S. K.

Generalized (?,?)-convexity in nonsmooth vector optimization over cones

S. K. SUNEJA, (University of Delhi, Delhi, India)

Sunila SHARMA, (University of Delhi, Delhi, India)

Malti KAPOOR (University of Delhi, Delhi, India)

An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

2 0

Yıl: 2016 Cilt: 6 Sayı: 1 Sayfa Aralığı: 1 - 8 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Generalized (?,?)-convexity in nonsmooth vector optimization over cones

Öz:

In this paper, new classes of cone-generalized (?,?)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes. Using these generalized functions, various sufficient Karush-Kuhn-Tucker (KKT) type nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used. Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (?,?)-convexity assumptions.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Antczak, T., On nonsmooth (?,?)- invexmultiobjective programming in finitedimensional Euclidean spaces, Journal of Advanced Mathematical Studies, 7, 127-145 (2014).
[2] Antczak, T., Stasiak, A., (?,?)-invexity in nonsmooth optimization, Numerical Functional Analysis and Optimization, 32(1), 1-25 (2010).
[3] Caristi, G., Ferrara, M., Stefanescu, A., Mathematical programming with (?,?)- invexity. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, 583, 167-176. Springer, Berlin-Heidelberg-New York (2006).
[4] Clarke, F. H., Optimization and Nonsmooth Analysis, Wiley, New York (1983).
[5] Craven, B. D., Nonsmooth multiobjective programming, Numerical Functional Analysis and Optimization, 10(1-2), 49-64 (1989).
[6] Ferrara, M., Stefanescu, M.V., Optimality conditions and duality in multiobjective programming with (?,?)-invexity. Yugoslav Journal of Operations Research, 18, 153-165 (2008)
[7] Hanson, M.A., On sufficiency of the KuhnTucker conditions, Journal of Mathematical Analysis and Applications, 80, 545-550 (1981).
[8] Hanson, M.A., Mond, B., Further generalization of convexity in mathematical programming. Journal of Information and Optimization Sciences, 3, 25-32 (1982).
[9] Preda, V., On efficiency and duality for multiobjective programs, Journal of Mathematical Analysis and Applications, 166, 365-377 (1992).
[10] Vial, J.P., Strong and weak convexity of sets and functions, Mathematics of Operations Research, 8, 231-259 (1983).

APA	SUNEJA S, SHARMA S, KAPOOR M (2016). Generalized (?,?)-convexity in nonsmooth vector optimization over cones. , 1 - 8.
Chicago	SUNEJA S. K.,SHARMA Sunila,KAPOOR Malti Generalized (?,?)-convexity in nonsmooth vector optimization over cones. (2016): 1 - 8.
MLA	SUNEJA S. K.,SHARMA Sunila,KAPOOR Malti Generalized (?,?)-convexity in nonsmooth vector optimization over cones. , 2016, ss.1 - 8.
AMA	SUNEJA S,SHARMA S,KAPOOR M Generalized (?,?)-convexity in nonsmooth vector optimization over cones. . 2016; 1 - 8.
Vancouver	SUNEJA S,SHARMA S,KAPOOR M Generalized (?,?)-convexity in nonsmooth vector optimization over cones. . 2016; 1 - 8.
IEEE	SUNEJA S,SHARMA S,KAPOOR M "Generalized (?,?)-convexity in nonsmooth vector optimization over cones." , ss.1 - 8, 2016.
ISNAD	SUNEJA, S. K. vd. "Generalized (?,?)-convexity in nonsmooth vector optimization over cones". (2016), 1-8.

APA	SUNEJA S, SHARMA S, KAPOOR M (2016). Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 6(1), 1 - 8.
Chicago	SUNEJA S. K.,SHARMA Sunila,KAPOOR Malti Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6, no.1 (2016): 1 - 8.
MLA	SUNEJA S. K.,SHARMA Sunila,KAPOOR Malti Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), vol.6, no.1, 2016, ss.1 - 8.
AMA	SUNEJA S,SHARMA S,KAPOOR M Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2016; 6(1): 1 - 8.
Vancouver	SUNEJA S,SHARMA S,KAPOOR M Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2016; 6(1): 1 - 8.
IEEE	SUNEJA S,SHARMA S,KAPOOR M "Generalized (?,?)-convexity in nonsmooth vector optimization over cones." An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 6, ss.1 - 8, 2016.
ISNAD	SUNEJA, S. K. vd. "Generalized (?,?)-convexity in nonsmooth vector optimization over cones". An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6/1 (2016), 1-8.