A generalized computing paradigm based on artificial dynamic models for mathematical programming

In this paper a novel computing paradigm aimed at solving non linear systems of equations and finding feasible solutions and local optima to scalar and multi objective optimizations problems is conceptualized. The underlying principle is to formulate a generic programming problem by a proper set of ordinary differential equations, whose equilibrium points correspond to the problem solutions. Starting from the Lyapunov theory, we will demonstrate that this artificial dynamic system could be designed to be stable with an exponential asymptotic convergence to equilibrium points. This important feature allows the analyst to overcome some of the inherent limitations of the traditional iterative solution algorithms that can fail to converge due to the highly nonlinearities of the first-order conditions. Besides we will demonstrate as the proposed paradigm could be applied to solve non linear equations systems, scalar and multi-objective optimization problems. Extensive numerical studies aimed at assessing the effectiveness of the proposed computing paradigm are presented and discussed.