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Optimality conditions for preinvex functions using symmetric derivative

Rastogi Sachin, Iqbal Akhlad, Rajan Sanjeev

Operations Research and Decisions

2022

Vol. 32, No. 4

91--101

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.

Some differential operators in the symmetric bundle

Kimaczyńska A.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 3

27--36

Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.