Mixed type second-order symmetric duality under F-convexity
We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.
[1] Ahmad, I., Multiobjective mixed symmetric duality with invexity, New Zealand Journal of Mathematics 34, 1-9 (2005).
[2] Ahmad, I., Husain, Z., Multiobjective mixed symmetric duality involving cones, Comput- ers and Mathematics with Applications, 59, 319-316 (2010).
[3] Bector, C. R., Chandra, S., Abha, On mixed symmetric duality in multiobjective programming, Opsearch 36, 399-407 (1999).
[4] Dantzig, G. B., Eisenberg, E., Cottle, R. W., Symmetric dual nonlinear programming, Pacific Journal of Mathematics 15, 809-812 (1965).
[5] Dorn, W. S., A symmetric dual theorem for quadratic programming, Journal of Op- erations Research Society of Japan 2, 93-97 (1960).
[6] Kailey, N., Gupta, S.K., Dangar, D., Mixed second-order multiobjective symmetric dual- ity with cone constraints, Nonlinear Analy- sis: Real World Applications 12, 3373-3383 (2011).
[7] Mangasarian, O. L., Nonlinear Program- ming, McGraw-Hill, New York (1969).
[8] Mangasarian, O. L., Second and higher-order duality in nonlinear programming, Journal of Mathematical Analysis and Applications 51, 607-620 (1975).
[9] Mond, B., Asymmetric dual theorem for non- linear programs, Quarterly Journal of Ap- plied Mathematics 23, 265-269 (1965).
[10] Mond, B., Second order duality for nonlinear programs, Opsearch 11, 90-99 (1974).
[11] Yang, X.M., Second order symmetric duality for nonlinear programs, Opsearch 32, 205-209 (1995).