An Exact Penalty Projected Structured Quasi-Newton Method for Constrained Nonlinear Least Squares

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Soradi Zeid, Samaneh | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42383 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezamoddin
Abstract:
This paper is concerned with the development, numerical implementation, and testing of an algorithm for solving constrained nonlinear least squares problems.The approach is based on the adaptive structured scheme of the exact penalty mehods first Proposed by Mahdavi-Amiri and Bartels and later extended by Mahdavi-Amiri and Ansari. The algorithm is an adaptation to the least squares case of an exact penalty method for solving nonlinearly constrained optimization problems due to Coleman and Conn. It also draws upon the methods of Nocedal and Overton for handling quasi-Newton updates of projected Hessian, upon the methods of Dennis, Gay, and Welsch for approaching the structure of nonlinear least squares Hessian. This method has been tested on a selection of problems listed in the collection of Schittkowski and Hock. We discuss the comparative results of the testing of this programs and three nonlinear programming codes from KNITRO on this collection
Keywords:
Nonlinear Least Squares ; Constrained Nonlinear Programming ; Exact Penalty Function ; Projected Structured Hessian Update