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Optimality conditions for preinvex functions using symmetric derivative

Author

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  • Sachin Rastogi
  • Akhlad Iqbal
  • Sanjeev Rajan

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.

Suggested Citation

  • Sachin Rastogi & Akhlad Iqbal & Sanjeev Rajan, 2022. "Optimality conditions for preinvex functions using symmetric derivative," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(4), pages 91-101.
    • Handle: RePEc:wut:journl:v:32:y:2022:i:4:p:91-101:id:6
    DOI: 10.37190/ord220406
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