Solution Of Bounded Nonlinear Systems Of Equations Using Homotopies With Inexact Restoration

Nonlinear systems of equations often represent mathematical models of chemical production processes and other engineering problems. Homotopic techniques (in particular, the bounded homotopies introduced by Paloschi) are used for enhancing convergence to solutions, especially when a good initial estimate is not available. In this paper, the homotopy curve is considered as the feasible set of a mathematical programming problem, where the objective is to find the optimal value of the homotopic parameter. Inexact restoration techniques can then be used to generate approximations in a neighborhood of the homotopy, the size of which is theoretically justified. Numerical examples are given.

Keywords:

• Nonlinear Programming
• Nonlinear Systems
• Homotopies
• Bounded Homotopies
• Homotopy Methods
• Inexact Restoration