Solving inequalities by alpha-dense curves. Application to global optimization
Purpose - To introduce an algorithm to solve inequalities defined by real functions on a certain compact set D of a general metric space (E, D). The device is based on a-dense curves. Design/methodology/approach - The solution of inequalities using a-dense curves and also an approach to a global optimization technique, similarly obtained to that of the inequalities. Findings - A new method is presented. The algorithm for solving inequalities is described which is based on a proven result. Inequalities of n-variable dependence are reduced by transformation using a-dense curves. Research limitations/implications - The research is a continuation of studies that resulted in a new method called Alienor for solving global optimization problems associated with multi-variable functions. Originality/value - Based on earlier research by the authors a-dense curves have been used which allow the transformation of a n-variables global optimization problem into a one-variable global one. This paper gives a new method for quickly solving the one-variable problem.
optimization techniques cybernetics programming and algorithm theory