Year: 1990
Author: Li-Xiang Jia
Journal of Computational Mathematics, Vol. 8 (1990), Iss. 3 : pp. 195–201
Abstract
This paper presents a detailed derivation and description of a new method for solving equality constrained optimization problem. The new method is based upon the quadratic penalty function, but uses orthogonal transformations, derived from the Jacobian matrix of the constraints, to deal with the numerical ill-conditioning that affects the methods of this type.
At each iteration of the new algorithm, the orthogonal search direction is determined by a quasi-Newton method which can avoid the necessity of solving a set of equations and the step-length is chosen by a Armijo line search. The matrix which approaches the inverse of the projected Hessian of composite function is updated by means of the BFGS formula from iteration to iteration. As the penalty parameter approaches zero, the projected inverse Hessian has special structure which can guarantee us to obtain the search direction accurately even if the Hessian of composite function is ill-conditioned in the former penalty function methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1990-JCM-9432
Journal of Computational Mathematics, Vol. 8 (1990), Iss. 3 : pp. 195–201
Published online: 1990-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7