Godwin NO Asemota

Keywords: computability, optimisation, partial functions, recursive functions, turing machines

Abstract: We shall show in this paper a class of computable convex functions, which have their first two solutions specified, and for which, all the polynomial solutions are uniquely determined. We shall also prove that the class of functions are convex, computable and represents a set of partial functions. Analyses indicate that it is double recursive, which can be composed from its primitive recursive functions. The class of convex functions can be shown to be reducible to Ackermann’s functions with some modifications to the algorithm, which lend themselves to computability in the form of Turing machines and ? -calculus, according to Church. Least search operator or minimisation conditions can be imposed on this class of functions, such that, either no solution is returned for a certain term of the function or a term for which, the solution is zero. However, this set of computable convex functions find application in solving optimisation problems in operations research, load and demand side management in electrical power systems engineering, switching operations in computer science and electronics engineering, mathematical logic and several other application areas in industry.

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