A two-step superlinearly convergent projected structured BFGS method for constrained nonlinear least squares

Abstract

We present an exact penalty approach for solving constrained non-linear least-squares problems, when the projected structured Hessian is approximated by a projected version of the structured BFGS formula and prove its local two-step Q-superlinear convergence. The numerical results obtained in an extensive comparative testing experiment confirm the approach to be reliable and efficient.

Keywords:

• structured secant methods
• constrained non-linear least squares
• exact penalty methods
• projected Hessian updates

Acknowledgements

The authors thank the Research Council of Sharif University of Technology for its support.