Numerical optimization techniques
Numerical optimization techniques
Numerical analysis: 4th ed
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical Methods
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
| Hi-index | 0.00 |
This paper describes an application of numerical methods to solve a continuous time non-linear optimal growth model with technology adoption. In the model, a non-convex production function arises from a threshold level of knowledge required to operate new technology. The study explains and illustrates how to compute the complete transition path of the growth model by applying in concert three broad numerical techniques in particular specialized ways, in order to maintain certain regularity conditions and restrictions of the model. The three broad techniques are: (i) Gauss-Laguerre quadrature for computing discounted utility over an infinite horizon; (ii) Fourth-Order Runge-Kutta method for solving differential equations; and (iii) the Penalty Functions method for solving the constrained optimization problem. The particular specializations involve linear interpolation for solving the optimal adoption time in the model and quasi-Newton iterations for maximizing the penalty-weighted objective function, the latter aided by grid search for determining initial values and Richardson extrapolation for approximating the gradient vector.