Volume 18, Issue 4 (12-2021)                   jor 2021, 18(4): 21-31 | Back to browse issues page

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Bidabadi N. Using an Efficient Penalty Method for Solving Linear Least Square Problem with Nonlinear Constraints. jor 2021; 18 (4) :21-31
URL: http://jamlu.liau.ac.ir/article-1-1453-en.html
Using an Efficient Penalty Method for Solving Linear Least Square Problem with Nonlinear Constraints
N. Bidabadi *
Yazd University, Department of Mathematical Sciences, Yazd, Iran , n_bidabadi@yazd.ac.ir
Abstract:   (1810 Views)
In this paper, we use a penalty method for solving the linear least squares problem with nonlinear constraints. In each iteration of penalty methods for solving the problem, the calculation of projected Hessian matrix is required. Given that the objective function is linear least squares, projected Hessian matrix of the penalty function consists of two parts that the exact amount of a part of it is in the hand, but the calculation of the other part is expensive. In this paper, after obtaining a structured secant relation, we use a structured quasi-Newton method to approximate the projected Hessian matrix and then, we show the asymptotic and global convergence of the presented method. The obtained numerical results show the efficiency of this method.
Keywords: Exact Penalty Method, Least Squares Problem, Structured Updating.
Full-Text [PDF 769 kb]   (545 Downloads)    
Type of Study: Applicable | Subject: Special
Received: 2020/09/6 | Accepted: 2021/05/12
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