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

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.