Accelerated Conjugate Direction Methods for Unconstrained Optimization.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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A family of accelerated conjugate direction methods, corresponding to the Broyden family of quasi-Newton methods, is described. It is shown that all members of the family generate the same sequence of points approximating the optimum and the same sequence of search directions, provided only that each direction vector is normalized before the step-size to be taken in that direction is determined. With minimal restrictions on how the step-size is determined sufficient only for convergence, the accelerated methods applied to the optimization of a function of n variables are shown to have an n1-step quadratic rate of convergence. Furthermore, the information needed to generate an accelerating step can be stored in a single n-vector, rather than the usual n X n symmetric matrix, without changing the theoretical order of convergence. The relationships between this family of methods and existing conjugate direction methods are discussed, and numerical experience with two members of the family is presented.
- Theoretical Mathematics