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ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS
- Source :
- Taiwanese J. Math. 17, no. 3 (2013), 833-855
- Publication Year :
- 2013
- Publisher :
- The Mathematical Society of the Republic of China, 2013.
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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.
- 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
Subjects
Details
- ISSN :
- 10275487
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Taiwanese Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....6f4814288c09b31137e1ca41b04bd7a8