Dynamic Control of Infeasibility for Nonlinear Programming

Abel S. Siqueira
Francisco A. M. Gomes Neto

An effective way of solving general nonlinear programming problems is the adoption of composite-step strategies that combine a step tangent to the constraints and a normal step, alternating between reducing the objective function value and the norm of the infeasibility. However, this kind of method requires the control of the iterates in order to prevent one step from destroying the progress of the other. In the Dynamic Control of Infeasibility algorithm, proposed by Bielschowsky and Gomes for equality constrained problems, the steps are controlled through the use of the so called Trust Cylinders. We present an extension of this algorithm for solving problems with general constraints. We also show numerical experiments that indicate that the new method has a performance that is comparable to well known nonlinear programing codes.

nonlinear programming
constrained optimization
numerical algorithms
interior point
Mathematics Subject Classification 2000 (MSC 2000): 
65K05 - 90C30