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On stability of the gradient algorithm in convex discrete optimisation problems and related questions
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A. B. Ramazanov
Veröffentlicht/Copyright:
15. November 2011
Abstract
We introduce the notion of steepness of a coordinate-convex function of discrete argument on an ordinal-convex set. In terms of guaranteed estimates it is shown that in problems of optimisation of coordinate-convex functions on an ordinal-convex set the gradient coordinatewise lifting algorithm is stable under small perturbations of the utility function. As corollaries we obtain improved guaranteed estimates for accuracy of the gradient algorithm, and also new sufficient conditions for the values of the utility function of the problem under consideration to coincide in the global and gradient extrema.
Received: 2009-07-09
Published Online: 2011-11-15
Published in Print: 2011-November
© de Gruyter 2011
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Artikel in diesem Heft
- Some nonequiprobable models of random permutations
- Automaton representation of a free group
- On estimation of the number of graphs in some hereditary classes
- An asymptotic upper bound for the chromatic index of random hypergraphs
- On stability of the gradient algorithm in convex discrete optimisation problems and related questions
- Rings over which all modules are completely integrally closed
- Lower bounds for complexity of Boolean circuits of finite depth with arbitrary elements
