Vector optimization with cone semilocally preinvex functions

In this paper we introduce cone semilocally preinvex, cone semilocally quasi preinvex and cone semilocally pseudo preinvex functions and study their properties. These functions are further used to establish necessary and sufficient optimality conditions for a vector minimization problem over cones. A Mond-Weir type dual is formulated for the vector optimization problem and various duality theorems are proved

PDF

___

[1] Ewing G.M., Sufficient Conditions for Global Minima of Suitable Convex Functional from Variational and Control Theory. SIAM Review 19, 202-220 (1977).
[2] Illes, T., Kassay, G., Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming. Journal of Optimization Theory and Applications 101(2), 243-257 (1999).
[3] Kaul, R.N., Kaur, S., Generalization of Convex and Related Functions. European Journal of Operational Research 9, 369- 377 (1982).
[4] Kaul, R.N., Kaur, S., Sufficient Optimality Conditions using Generalized Convex Functions. Opsearch 19, 212-224 (1982).
[5] Kaul, R.N., Kaur, S., Generalized Convex Functions, Properties, Optimality and Duality. Technical Report, SOL., 84-4, Stanford University, California (1984).
[6] Kaul, R.N., Lyall, V., Kaur, S., Semilocal Pseudolinearity and Efficiency. European Journal of Operational Research 36, 402- 409 (1988).
[7] Kaur, S., Theoretical Studies in Mathematical Programming. Ph.D. Thesis, University of Delhi, Delhi, India (1983).
[8] Gupta, I., Vartak, M.N., Kuhn-Tucker and Fritz John Type Sufficient Optimality Conditions for Generalized Semilocally Convex Programs. Opsearch 26, 11-27 (1989).
[9] Mukherjee, R.N., Mishra, S.K., Multiobjective Programming with Semilocally Convex Functions. Journal of Mathematical Analysis and Applications. 199, 409-424 (1996).
[10] Preda, V., Optimality Conditions and Duality in Multiobjective Programming Involving Semilocally Convex and Related Functions. Optimization 36, 219- 230 (1996).
[11] Preda, V., Optimality and Duality in Fractional Multiobjective Programming involving Semilocally Preinvex and Related Functions. Journal of Mathematical Analysis and Applications 288, 365-382 (2003).
[12] Preda V., Stancu-Minasian, J.M., Duality in Multiobjective Programming involving Semilocally Preinvex and Related Functions. Glas. Math. 32, 153-165 (1997).
[13] Stancu-Minasian, J.M., Optimality and Duality in Fractional Programming involving Semilocally Preinvex and Related Functions. Journal of Information and Optimization Science 23, 185-201 (2002).
[14] Suneja, S.K., Gupta, S., Duality in Nonlinear Programming involving Semilocally Convex and Related Functions. Optimization 28, 17-29 (1993).
[15] Suneja, S.K., Gupta, S., Vani, Optimality and Duality in Multiobjective Nonlinear programming involving  -Semilocally Preinvex and Related Functions. Opsearch 44(1), 27-40 (2007).
[16] Weir, T., Programming with Semilocally Convex Functions. Journal of Mathematical Analysis and Applications 168 (1-2), 1-12 (1992).

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

ISSN: 2146-0957
Yayın Aralığı: Yılda 2 Sayı
Yayıncı: Prof. Dr. Ramazan YAMAN

Arşiv

Sayıdaki Diğer Makaleler

Economic production quantity (EPQ) model for three type imperfect items with rework and learning in setup

Arindum MUKHOPADHYAY, Adrijit GOSWAMİ

Vector optimization with cone semilocally preinvex functions

Surjeet Kaur SUNEJA, Meetu BHATİA

Mond-Weir type second order multimixed symmetric duality with square root term under generalized univex function

Arun Kumar TRİPATHY

A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization

Hehua JİAO

Multi-choice stochastic transportation problem involving Weibull distribution

Deshabrata Roy MAHAPATRA

Vector variational inequalities and their relations with vector optimization

Surjeet Kaur SUNEJAA, Bhawna KOHLİ