Projection method for unconstrained optimization
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A method of conjugate directions, the projection method, for solving unconstrained minimization problems is presented. Under the assumption of uniform strict convexity, the method is shown to converge to the global minimizer of the unconstrained problem and to have an (n − 1)-step superlinear rate of convergence. With a Lipschitz condition on the second derivatives, the rate of convergence is shown to be a modifiedn-step quadratic one.
KeywordsMinimization Problem Global Minimizer Projection Method Lipschitz Condition Unconstrained Optimization
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- 1.Zoutendijk, G.,Methods of Feasible Directions, Elsevier Publishing Company, Amsterdam, Holland, 1960.Google Scholar
- 2.Goldstein, A. A.,Constructive Real Analysis, Harper and Row, Publishers, New York, 1967.Google Scholar
- 3.Vainberg, M. M.,Variational Methods for the Study of Nonlinear Operations, Holden-Day, San Francisco, 1964.Google Scholar
- 4.Dieudonné, J.,Foundations of Modern Analysis, Academic Press, New York, 1960.Google Scholar
- 5.McCormick, G. P., andPearson, J. D.,Varable Metric Methods and Unconstrained Optimization, Optimization, Edited by R. Fletcher, Academic Press, New York, 1968.Google Scholar
- 6.Pearson, J. D.,Variable Metric Methods of Minimization, Computer Journal, Vol. 12, No. 2, 1969.Google Scholar
- 7.Zoutendijk, G.,Some Algorithms Based on the Principle of Feasible Directions, Nonlinear Programming, Edited by J. B. Rosen, O. L. Mangasarian, and K. Ritter, K. Ritter, Academic Press, New York, M970.Google Scholar
- 8.McCormick, G. P., andRitter, K.,On the Convergence and Rate of Convergence of the Conjugate Gradient Method, University of Wisconsin, Mathematics Research Center, MRC Report No. 1118, 1970.Google Scholar
- 9.McCormick, G. P., andRitter, K.,Methods of Conjugate Directions versus Quasi-Newton Methods, Research Analysis Corporation, McLean, Virginia, Report No. RAC-TP-433, 1971.Google Scholar
- 10.Goldfarb, D.,Extension of Davidon's Variable Metric Method to Maximization Under Linear Inequality and Equality Constraint, SIAM Journal on Applied Mathematics, Vol. 17, No. 4, 1969.Google Scholar