Methods of generalized descent
The idea behind these methods is rather simple and obvious. Their algorithmical realization may be reduced to the choice a of local minimization algorithm and of auxiliary functions whose minimization gives conditions under which better local minima of f(·) may successively be found. The auxilary functions are constructed using the objective function and penalty functions.
However, the auxilary functions normally become rather flat and are therefore difficult to minimize. An exception to this are algebraic objective functions but in practice such functions are rare.
Further research is necessary to define more precisely the class of functions to which the algorithms of the considered type may be efficiently applied. An important problem to be solved is how to ensure the numerical stability of the exploited local minimization algorithms when applied to flat functions.
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