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Variable Metric Optimization Method
The Variable Metric optimization method is basically a multidimensional version of the Quadratic Approximations method. The basic idea is to fit the objective function to a quadratic function of all independent variables. The quadratic function is then differentiated and set to zero to locate a new trial point. An algorithm for the Variable Metric method is presented in Numerical Recipes, by Press et al, Cambridge University Press, 1989. The method necessarily requires numerical derivatives. In fact, second derivatives (the Hessian matrix) are needed which may cause problems in some circumstances when the equations are not solved to tight tolerances. As with the Quadratic Approximations method, when the Variable Metric method works, it works well and it is usually more efficient than the Conjugate Directions method implementation in EES. The algorithm is implemented in the following manner.
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