Titlebook: Numerical Optimization with Computational Errors; Alexander J. Zaslavski Book 2016 Springer International Publishing Switzerland 2016 nonl

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The Extragradient Method for Solving Variational Inequalities,errors. The convergence of the subgradient method for solving variational inequalities is established for nonsummable computational errors. We show that the subgradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.

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Continuous Subgradient Method,w that our algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how much time one needs for this.

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,Newton’s Method,ich appear in the right-hand side of the equations, are not necessarily differentiable. Our goal is to obtain an approximate solution in the presence of computational errors. In order to meet this goal, in the case of inclusions, we study the behavior of iterates of nonexpansive set-valued mappings

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Alexander J. Zaslavskiaccounts, the next generation of supercomputers will achieve its gains by increasing the number of processing elements, rather than by using faster processors. The most difficult technical problem in constructing a supercom- puter will be the design of the interconnection network through which the p