Best proximity point theorems: unriddling a special nonlinear programming problem

This paper addresses the non-linear programming problem of globally minimizing the real valued function x ⟶ d ( x , Sx ) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event...

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Bibliographic Details
Published in:TOP Vol. 22; no. 2; pp. 543 - 553
Main Author: Sadiq Basha, S.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2014
Subjects:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
Generalized proximal contraction
Non-linear programming problem
Global optimization
90C30
Generalized proximal cyclic contraction
Optimal approximate solution
Proximal contraction
Proximal cyclic contraction
90C26
Best proximity point
Fixed point
ISSN:1134-5764, 1863-8279
Online Access:Get full text
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Summary:This paper addresses the non-linear programming problem of globally minimizing the real valued function x ⟶ d ( x , Sx ) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event that they have no solution.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-012-0269-1