Abstract
A uniform randomized exponential-potential block-coordinate descent method for the approximate solution of block-angular convex resource-sharing programs was analyzed in [5] and for the linear case in [14]. The former method is rendered deterministic by replacing its random block selection by arbitrary sweeps of its block coordinates, akin to classical implementations of Gauss-Seidel relaxation and coordinate descent in unconstrained optimization, recently used in concurrent network flows [15]. The general block-angular model consists of K disjoint convex compact sets (“blocks”) and M nonnegative convex block-separable inequalities (“coupling constraints”). It is shown that for linear coupling constraints and for a given but arbitrary relative accuracy ε ∈ (0, 1], the proposed derandomized algorithm runs in O(K ln M(ε −2 + ln min{K, M}) coordination steps or block optimizations, which is lower than all other existing bounds. It is also shown that this bound on coordination steps also applies to a reformulation of the above general nonlinear problem.
Research supported by the National Science Foundation under grant CCR-9208539.
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Villavicencio, J., Grigoriadis, M.D. (1996). Approximate Structured Optimization by Cyclic Block-Coordinate Descent. In: Fischer, H., Riedmüller, B., Schäffler, S. (eds) Applied Mathematics and Parallel Computing. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-99789-1_25
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DOI: https://doi.org/10.1007/978-3-642-99789-1_25
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