Issue: 2022/Vol.32/No.4, Pages 91-101
OPTIMALITY CONDITIONS FOR PREINVEX FUNCTIONS USING SYMMETRIC DERIVATIVE
Sachin Rastogi
, Akhlad Iqbal , Sanjeev Rajan
Cite as: S. Rastogi, A. Iqbal, S. Rajan. Optimality conditions for preinvex functions using symmetric derivative. Operations Research and Decisions 2022: 32(4), 91-101. DOI 10.37190/ord220406
Abstract
As a generalization of convex functions and derivatives, in this paper, the authors study the concept of a symmetric derivative for preinvex functions. Using symmetrical differentiation, they discuss an important characterization for preinvex functions and define symmetrically pseudo-invex and symmetrically quasi-invex functions. They also generalize the first derivative theorem for symmetrically differentiable functions and establish some relationships between symmetrically pseudo-invex and symmetrically quasi-invex functions. They also discuss the Fritz John type optimality conditions for preinvex, symmetrically pseudo-invex and symmetrically quasi-invex functions using symmetrical differentiability.
Keywords: invex sets, preinvex functions, symmetric derivative, Fritz John optimality conditions
Received: 19 April 2022 Accepted: 12 December 2022
Published online: 8 February 2023