Solving a Paraboloidally Constrained Quadratic Programming Using Parabola-Quadratic Programming

Abstract

In this paper, we discuss the state-of-the-art models in estimating, evaluating, and selecting among non-linear mathematical models for obtaining the optimal solution of the optimization problems which involve the nonlinear functions in their constraints. We review theoretical and empirical issues including Newton's method, linear programming, quadratic programming, quadratically constrained programming, parabola, circle and the relation between parabola and circle. Finally, we outline our method called parabola-quadratic programming which is useful for solving economic forecasting and financial time-series with non-linear models. Keywords: Parabola; Circle; Quadratic; Optimization; Algorithm. 2010 Mathematics Subject Classification: 90C30