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Adaptive Algorithm for Constrained Least-Squares Problems
Authors:Li  ZF  Osborne  MR  Prvan  T
Institution:(1) National Centre for Epidemiology and Population Health, Australian National University, Canberra, Australia;(2) School of Mathematical Sciences, Australian National University, Canberra, Australia;(3) School of Mathematics and Statistics, University of Canberra, Canberra, Australia
Abstract:This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.
Keywords:constrained optimization  nonlinear least squares  SQP methods  Gauss–  Newton approximation  quasi-Newton method
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