Multiple cuts in separating plane algorithms

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 and it is shown that it requires … Read more

Fejer processes with diminishing disturbances and decomposition of constrained nondifferentiable optimization problems

Iterative processes based on Fejer mappings with diminishing problem-specific shifts in the arguments are considered. Such structure allows fine-tuning of Fejer processes by directing them toward selected subsets of attracting sets. Use of various Fejer operators provides ample opportunities for decomposition and parallel computations. Subgradient projection algorithms with sequential and simultaneous projections on segmented constraints … Read more