Constrained Nonlinear Least Squares: A Superlinearly Convergent Projected Structured Secant Method
نویسندگان
چکیده
Numerical solution of nonlinear least-squares problems is an important computational task in science and engineering. Effective algorithms have been developed for solving nonlinear least squares problems. The structured secant method is a class of efficient methods developed in recent years for optimization problems in which the Hessian of the objective function has some special structure. A primary and typical application of the structured secant method is to solve the nonlinear least squares problems. We present an exact penalty method for solving constrained nonlinear leastsquares problems, when the structured projected Hessian is approximated by a projected version of the structured BFGS formula and give its local two-step Q-superlinear convergence. For robustness, we employ a special nonsmooth line search strategy, taking account of the least squares objective. 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 MahdaviAmiri. Numerical results also confirm the practical relevance of our special considerations for the inherent structure of the least squares.
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