1. Partitioned multiply scaled pseudo conjugate gradient schemes
- Author
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Y. H. Guo, Lala B. Krishna, and Joseph Padovan
- Subjects
Mathematical optimization ,business.industry ,Applied Mathematics ,Mechanical Engineering ,Computational Mechanics ,Block matrix ,Ocean Engineering ,Nonlinear conjugate gradient method ,Maxima and minima ,Computational Mathematics ,Computational Theory and Mathematics ,Orthogonality ,Iterated function ,Robustness (computer science) ,Conjugate gradient method ,Applied mathematics ,Local search (optimization) ,business ,Mathematics - Abstract
Through the introduction of multiple two parameter pairs of scaling factors, a modified formulation of the conjugate gradient scheme is derived. The individual pairs are separately assigned to the various substructure of a model so as to gauge the optimal local search direction and length. During the iteration process, this yields a successions of multiparameter dependent energy states. Seeking the appropriate minima, a vectorized multiparameter formulation of the conjugate gradient scheme is derived. Due to the manner of formulation, the scheme provides both global as well as substructural level orthogonality among successive iterates. To generalize the scheme, both pre and unpreconditioned versions are developed. Overall the methodology provides a potentially significant improvement in computational robustness. This is benchmarked in a series of numerical experiments.
- Published
- 1991