Efficient generalized conjugate gradient algorithms, part 2: Implementation
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In Part 1 of this paper (Ref. 1), a new, generalized conjugate gradient algorithm was proposed and its convergence investigated. In this second part, the new algorithm is compared numerically with other modified conjugate gradient methods and with limited-memory quasi-Newton methods.
Key WordsUnconstrained optimization hybrid and restart conjugate gradient methods limited-memory methods inexact line search
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- 1.Liu, Y., andStorey, C.,Efficient Generalized Conjugate Gradient Algorithms, Part 1, Theory, Journal of Optimization Theory and Applications, Vol. 69, No. 1, pp. 129–137, 1991.Google Scholar
- 2.Dixon, L. C. W., Ducksbury, P. G., andSingh, P.,A New Three-Term Conjugate Gradient Method, Technical Report No. 130, Numerical Optimization Centre, Hatfield Polytechnic, Hatfield, Hertfordshire, England, 1985.Google Scholar
- 3.Liu, D. C., andNocedal, J.,On the Limited-Memory BFGS Method for Large-Scale Optimization, Technical Report No. NAM-03, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois, 1988.Google Scholar
- 4.Nazareth, J. L.,Conjugate Gradient Methods Less Dependent on Conjugacy, SIAM Review, Vol. 28, pp. 501–511, 1986.Google Scholar
- 5.Nazareth, J. L.,The Method of Successive Affine Reduction for Nonlinear Minimization, Mathematical Programming, Vol. 35, pp. 97–109, 1986.Google Scholar
- 6.Powell, M. J. D.,Restart Procedures for the Conjugate Gradient Method, Mathematical Programming, Vol. 12, pp. 241–254, 1977.Google Scholar
- 7.Cohan, A.,Rate of Convergence of Several Conjugate Gradient Algorithms, SIAM Journal on Numerical Analysis, Vol. 9, pp. 248–259, 1972.Google Scholar