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Fejer processes are frequently used models for many iterative algorithms in optimization and related areas. They can be combined with different kinds of decomposition schemes and generate various projection-type methods suitable for parallel computations. This paper reviews some recent results on Fejer processes with diminishing disturbances and suggests a(More)
This paper presents an extended version of the separation plane algorithms for subgradient-based finite-dimensional nondifferentiable convex blackbox optimization. The extension introduces additional cuts for epigraph of the conjugate of objective function which improve the convergence of the algorithm. The case of affine cuts is considered in more details(More)
Problems of finding an arbitrary point of convex feasible set (convex feasibility problem, CFP), stationary points of monotone mappings (convex optimization, variational inequalities) are quite common objects of investigation in theory and applications [1]. One of the unifying themes for algorithmic developments in these areas are Fejer processes [2] which(More)
A modification of the ellipsoid method (EM) is considered. This modification (MEM) is asymptotically equivalent to the original EM for large-scale problems but applicable to lower dimensions down to one-dimensional case. MEM preserves close to EM volume reduction factors for all dimensions and gives close to optimal 0.5 accuracy improving multiplier for 1d.(More)
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