A variable metric algorithm for constrained minimization based on an augmented Lagrangian

Abstract

This paper concerns the implementation of a recent idea, attributed to Hestenes and Powell, based on solving the equality constrained finite dimensional minimization problemwhere f is a non-linear functional, g is a non-linear mapping into R p , K is a prescribed matrix of penalty constants and 1 is the Lagrange multiplier. The computational algorithm is based on restoring active constraints to first order and adjusting x in the remaining necessary conditions by gradient projection. The minimization is performed by the variable metric rank-two BGFS update with linear search by cubic interpolation. Computational results using the algorithm include two problems of minimum fuel trajectory optimization-two impulse rendezvous with Comet Encke and three impulse constrained positioning of a geostationary satellite.