Conjugate gradient algorithms for conic functions. (English) Zbl 0622.65045
The conjugate gradient method is modified to deal with the unconstrained optimization of the conic function in a finite number of steps. Based on a more general class of model functions, further extension of the method is provided.
A class of functions generalizing the quadratic function contains the conic functions introduced by various authors (e.g., Bjorstad and Nocedal (1980), Davidson (1980), Sorensen (1980), etc.). The current effort aims to modify the existing conjugate gradient method for minimizing conic functions. Results in regard to conic functions and interpolations are first derived. A comprehensive treatment of the derivation and analysis of the proposed method is provided. A new algorithm is described, which finds a minimum of the conic function after a finite number of perfect steps in the regular case. This is followed by the investigation of an imperfect version of the method. The last section proposes further extension of the conjugate gradient method based on a ore general class of model functions.
A class of functions generalizing the quadratic function contains the conic functions introduced by various authors (e.g., Bjorstad and Nocedal (1980), Davidson (1980), Sorensen (1980), etc.). The current effort aims to modify the existing conjugate gradient method for minimizing conic functions. Results in regard to conic functions and interpolations are first derived. A comprehensive treatment of the derivation and analysis of the proposed method is provided. A new algorithm is described, which finds a minimum of the conic function after a finite number of perfect steps in the regular case. This is followed by the investigation of an imperfect version of the method. The last section proposes further extension of the conjugate gradient method based on a ore general class of model functions.
Reviewer: N.A.Warsi
Keywords:
conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithmReferences:
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