Abstract
Recently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established 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. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling the quasi-Newton updates of projected Hessians and appropriates the structuring scheme of Dennis, Martinez and Tapia. Here, for robustness, we present a specific nonsmooth line search strategy, taking account of the least squares objective. We also discuss the details of our new nonsmooth line search strategy, implementation details of the algorithm, and provide comparative results obtained by the testing of our program and three nonlinear programming codes from KNITRO on test problems (both small and large residuals) from Hock and Schittkowski, Lukšan and Vlček and some randomly generated ones due to Bartels and Mahdavi-Amiri. The results indeed affirm the practical relevance of our special considerations for the inherent structure of the least squares.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol17iss1pp103-124
- Journal
- Sultan Qaboos University Journal for Science, 16, 103
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Mahdavi‐Amiri, N., & Ansari, M. R. (2012). A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares. Sultan Qaboos University Journal for Science, 16, 103. https://doi.org/10.24200/squjs.vol17iss1pp103-124
MLA 9
Mahdavi‐Amiri, Nezam, and Mohammad Reza Ansari. "A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares." Sultan Qaboos University Journal for Science, vol. 16, 2012, pp. 103. https://doi.org/10.24200/squjs.vol17iss1pp103-124.
Chicago (author–date)
Mahdavi‐Amiri, Nezam, and Mohammad Reza Ansari. 2012. "A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares." Sultan Qaboos University Journal for Science 16: 103. https://doi.org/10.24200/squjs.vol17iss1pp103-124.
Harvard
Mahdavi‐Amiri, N. and Ansari, M. R. (2012) 'A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares', Sultan Qaboos University Journal for Science, 16, pp. 103. doi:10.24200/squjs.vol17iss1pp103-124.
Vancouver
Mahdavi‐Amiri N, Ansari MR. A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares. Sultan Qaboos University Journal for Science. 2012;16:103. doi:10.24200/squjs.vol17iss1pp103-124
IEEE
N. Mahdavi‐Amiri, and M. R. Ansari, "A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares," Sultan Qaboos University Journal for Science, vol. 16, pp. 103, 2012, doi: 10.24200/squjs.vol17iss1pp103-124.