Stochastic Solution on Convergence Property of Quadratic Functions

Abstract

Constraints satisfaction problems (CSPs) aim at solution via algorithms that search a domain space for goal states. The solution of which must satisfy all constraints and guarantees explicit reasoning structure that conveys data about the problem to the algorithm. Thus, it assigns to an output, a set of variables that satisfies a set of constraints in its bid to prune off huge portion of the search space. This study presents solutions to quadratic functions via David Fletcher Powell method and stochastic method of optimization. To aim this purpose, hybrid neural networks are trained using DFP as a pre-processor to yield approximate solutions to the quadratic function. A trial solution of the quadratic equation is written as sum of two parts: (a) first part satisfies the initial condition for unconstrained optimization using DFP and hybrids as separate methods to solve a quadratic function; while (b) second part uses DFP as a pre-processor with adjustable parameters of for the ANN-TLRN hybrid. Results show that presented method introduces a closer form to the analytic solution. These present method is easily extended to solve a wide range of problems.