Best proximity point theorems: exposition of a significant non-linear programming problem

S. Sadiq Basha (), N. Shahzad () and R. Jeyaraj ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1699-1705

Abstract: The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x → d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm is presented to determine a solution of the preceding non-linear programming problem that focuses on global optimization. As a sequel, one can compute optimal approximate solutions to some fixed point equations and optimal solutions to some unconstrained non-linear programming problems. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Global optimization; Non-linear programming problem; Best proximity point; Optimal approximate solution; Generalized proximal contraction; Proximal contraction; Fixed point (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9975-3

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