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On properties of geodesic semilocal E-preinvex functions
11Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, Serdang, Malaysia.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study introduces geodesic semilocal E-preinvex functions on Riemannian manifolds. New optimality conditions and duality results are established for nonlinear fractional multiobjective programming problems.
Area of Science:
- Optimization Theory
- Differential Geometry
- Mathematical Programming
Background:
- Generalizing existing function classes is crucial for advancing optimization theory.
- Riemannian manifolds provide a rich geometric framework for complex optimization problems.
- Nonlinear fractional multiobjective programming presents significant theoretical and computational challenges.
Purpose of the Study:
- To define and investigate geodesic semilocal E-preinvex functions on Riemannian manifolds.
- To establish sufficient optimality conditions for a class of nonlinear fractional multiobjective programming problems.
- To formulate and prove duality results using newly defined function classes.
Main Methods:
- Definition of geodesic semilocal E-preinvex functions.
- Application of geodesic E-η-semidifferentiability concepts.
- Formulation of dual problems and proof of duality theorems.
Main Results:
- Properties of geodesic semilocal E-preinvex functions are established.
- Sufficient optimality conditions for nonlinear fractional multiobjective programming are derived.
- Duality results are proven using geodesic semilocal, pseudo-semilocal, and quasi-semilocal E-preinvex functions.
Conclusions:
- The introduced function class offers a valuable generalization in optimization.
- The derived optimality and duality results advance the understanding of nonlinear fractional multiobjective programming.
- This work provides a solid foundation for future research in geometric optimization.
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