This paper introduces tensor methods for nonlinear equality constraine
d optimization problems. These are general purpose methods intended es
pecially for problems where the constraint gradient matrix at the solu
tion is rank deficient or ill conditioned. The new methods are adapted
from the standard successive quadratic programming method by augmenti
ng the linear model of the constraints with a simple second-order term
. The second-order term is selected so that the model of the constrain
ts interpolates constraint function values from one or more previous i
terations, as well as the current constraint function value and gradie
nts. Similar to tensor methods for nonlinear equations, the tensor met
hods for constrained optimization require no more function and derivat
ive evaluations, and hardly more storage or arithmetic per iteration,
than the standard SQP methods. Test results indicate that the tensor m
ethods are more efficient than SQP methods on singular and nonsingular
nonlinear equality constrained optimization problems, with a particul
arly large advantage on singular problems.