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Conjugate Gradient

There are eight different variants of CG in JETNET 3.0. Both standard CG ( MSTJN(5) = ) (eq. (gif)) and Scaled CG ( MSTJN(5) = (eq. (gif)) come with the four different options in eq. (gif) for computing the next search direction. The CG parameters, which control the line search etc., are described in a separate section below. The SCG parameters are PARJN(28) and PARJN(29). They correspond to the step used in computing the difference approximation s in eq. (gif) and to the initial value used for , respectively. The default values for these parameters usually work fine and the user should not need to set any parameters when using SCG, although the algorithm is sometimes speeded up by increasing PARJN(28).

The SCG runs best in combination with the Polak-Ribière formula for computing the next search direction ( MSTJN(5)=10). The CG algorithm, with line search, runs best with the Polak-Ribière ( MSTJN(5)=4) or Hestenes-Stiefel ( MSTJN(5)=5) formulas. However, the Shanno formula is designed to always guarantee a descent direction and is hence more robust (but slower).

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Fri Feb 24 11:28:59 MET 1995