X. M. Yang

Generalized invexity and generalized invariant monotonicity

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.

Characterizations and applications of prequasi-invex functions

In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems.

Second order symmetric duality in non-differentiable multiobjective programming with F-convexity

Abstract This paper is concerned with a pair of Mond–Weir type second order symmetric dual non-differentiable multiobjective programming problems. We establish the weak and strong duality theorems for the new pair of dual models under second order F -convexity assumptions. Several results including many recent works are obtained as special cases.

Second-order symmetric duality in multiobjective programming

Abstract A pair of second-order symmetric dual models for multiobjective nonlinear programming is proposed in this paper. We prove the weak, strong, and converse duality theorems for the formulated second-order symmetric dual programs under invexity conditions.

Huard type second-order converse duality for nonlinear programming ✩

In this paper, we establish a Huard type converse duality for a second-order dual model in nonlinear programming using Fritz John necessary optimality conditions.

Converse duality in nonlinear programming with cone constraints

Abstract The purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by Chandra and Abha [S. Chandra, Abha, A note on pseudo-invex and duality in nonlinear programming, European Journal of Operational Research 122 (2000) 161–165].

Erratum to “Huard type second-order converse duality for nonlinear programming” [Appl. Math. Lett. 18 (2005) 205–208]

Abstract T.R. Gulati and Divya Agarwal pointed out that the statement: α > 0 and θ = α r ∗ imply θ > 0 , on line 4 of page 208 of [X.M. Yang, X.Q. Yang and K.L. Teo, Appl. Math. Lett. 18 (2005) 205–208], is erroneous since θ = α r ∗ is obtained letting α = 0 . Here is a simple proof that θ > 0 .

Erratum to "Huard type second-order converse duality for nonlinear programming" [Appl. Math. Lett. 18 (2005) 205-208] (DOI:10.1016/j.aml.2004.04.008)

Abstract T.R. Gulati and Divya Agarwal pointed out that the statement: α > 0 and θ = α r ∗ imply θ > 0 , on line 4 of page 208 of [X.M. Yang, X.Q. Yang and K.L. Teo, Appl. Math. Lett. 18 (2005) 205–208], is erroneous since θ = α r ∗ is obtained letting α = 0 . Here is a simple proof that θ > 0 .