Abstract
The paper examines methods for increasing the dimension of a quasi-Newton approximation to a Hessian matrix when the dimension of the problem is increased. A new method is proposed, and numerical results given to demonstrate the superiority of the new method to existing methods.
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Draper, N. R., andSmith, H.,Applied Regression Analysis, John Wiley and Sons, New York, New York, 1966.
Murtagh, B. A., andSaunders, M. A.,Large-Scale Linearly Constrained Optimization, Mathematical Programming, Vol. 14, pp. 41–72, 1978.
Dennis, J. E., Gay, D. M., andWelsch, R. E.,An Adaptive Nonlinear Least-Squares Algorithm, Transactions on Mathematical Software, Vol. 7, pp. 348–368, 1981.
Shanno, D. F., andPhua, K. H.,Matrix Conditioning and Nonlinear Optimization, Mathematical Programming, Vol. 14, pp. 149–160, 1978.
Shanno, D. F., andPhua, K. H.,Remark on Algorithm 500, Transactions on Mathematical Software, Vol. 6, pp. 618–622, 1980.
Oren, S. S., andLuenberger, D. E.,Self-Scaling Variable Metric (SSVM) Algorithms, Part 1: Criteria and Sufficient Conditions for Scaling a Class of Algorithms, Management Science, Vol. 20, pp. 845–862, 1974.
Oren, S. S.,Self-Scaling Variable Metric (SSVM) Algorithms, Part 2: Implementation and Experiments, Management Science, Vol. 20, pp. 863–874, 1974.
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The work of the first author was partially supported by the Air Force Office of Scientific Research under Grant No. AFOSR-86-0170.
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Shanno, D.F., Phua, K.H. Adding variables to quasi-Newton Hessian approximations. J Optim Theory Appl 54, 575–582 (1987). https://doi.org/10.1007/BF00940203
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DOI: https://doi.org/10.1007/BF00940203