TENSOR METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION

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.