1. ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS
- Author
-
Li-wen Zhou and Nan-Jing Huang
- Subjects
nonlinear optimization problem ,Optimization problem ,Geodesic ,General Mathematics ,Geodesic map ,Regular polygon ,Mond-weir type dual ,Hadamard manifold ,Type (model theory) ,roughly geodesic $B$-invex set ,Nonlinear programming ,Combinatorics ,roughly geodesic $B$-invex function ,54H25 ,Hadamard transform ,Mathematics::Metric Geometry ,Mathematics::Differential Geometry ,49J40 ,Mathematics - Abstract
In this paper, a new class of roughly geodesic $B$-invex sets, quasi roughly geodesic $B$-invex functions and pseudo roughly geodesic $B$-invex functions are introduced and studied on Hadamard manifolds by relaxing the definitions of geodesic convex sets and functions. Some properties of quasi roughly geodesic $B$-invex functions and pseudo roughly geodesic $B$-invex functions are proved on Hadamard manifolds. As applications, some sufficient and necessary conditions for optimal solution of the nonlinear programming problems involving the quasi roughly geodesic $B$-invex functions and the pseudo roughly geodesic $B$-invex functions are given on Hadamard manifolds. The Mond-weir type dual problems for the nonlinear programming problems are also considered on Hadamard manifolds.
- Published
- 2013