Superlinearly convergent exact penalty projected structured Hessian updating schemes for constrained nonlinear least squares: asymptotic analysis

Mahdavi-Amiri, N.; Ansari, Mohammad Reza

Superlinearly convergent exact penalty projected structured Hessian updating schemes for constrained nonlinear least squares: asymptotic analysis

Document Type : Research Paper

Authors

N. Mahdavi-Amiri

Mohammad Reza Ansari

Sharif University of Technology

Abstract

We present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling the quasi-Newton updates of projected Hessians. We discuss the comparative results of the testing of our programs and three nonlinear programming codes from KNITRO on
some randomly generated test problems due to Bartels and Mahdavi-Amiri. The results indeed confirm the practical significance of our special considerations for the inherent structure of the least squares.

Keywords

Constrained nonlinear programming

exact penalty method

nonlinear least squares

projected structured Hessian update

Subjects