Fletcher optimization

Convergence behaviour of step-restricted augmented Hessian calculations (Fletcher optimization). 

Fletcher R 1981 Practical Methods of Optimization Vol 1—Unconstrained Optimization (New York Wley)... 

Within some programs, the ROMPn methods do not support analytic gradients. Thus, the fastest way to run the calculation is as a single point energy calculation with a geometry from another method. If a geometry optimization must be done at this level of theory, a non-gradient-based method such as the Fletcher-Powell optimization should be used. 

Davidsou-Fletcher-Powell (DFP) a geometry optimization algorithm De Novo algorithms algorithms that apply artificial intelligence or rational techniques to solving chemical problems density functional theory (DFT) a computational method based on the total electron density... 

Fletcher, R. Practical Methods of Optimization, John Wiley Sons, New York, 1980... 

Fletcher, R. Fractical Method of Optimization, Wiley, New York (1987). 

A more detailed discussion of such methods can be found in specialist books dealing with optimization (Fletcher, 1981 Powell, 1985). 

Figure 16 Root-mean-squared error progression plot for Fletcher nonlinear optimization and back-propagation algorithms during training.

Let II II denote the Euclidean norm and define = gk+i gk- Table I provides a chronological list of some choices for the CG update parameter. If the objective function is a strongly convex quadratic, then in theory, with an exact line search, all seven choices for the update parameter in Table I are equivalent. For a nonquadratic objective functional J (the ordinary situation in optimal control calculations), each choice for the update parameter leads to a different performance. A detailed discussion of the various CG methods is beyond the scope of this chapter. The reader is referred to Ref. [194] for a survey of CG methods. Here we only mention briefly that despite the strong convergence theory that has been developed for the Fletcher-Reeves, [195],... 

Abadie, J. and J. Carpentier. Generalization of the Wolfe Reduced Gradient Method to the Case of Nonlinear Constraints. In Optimization, R. Fletcher, ed. Academic Press, New York (1969), pp. 37-47. 

Do at least one simplex optimization before doing a Fletcher-Powell optimization. 

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