Abstract
In this chapter we analyze the convergence of the mirror descent algorithm under the presence of computational errors. We show that the 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 many iterates one needs for this.
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References
Beck A, Teboulle M (2003) Mirror descent and nonlinear projected subgradient methods for convex optimization. Oper Res Lett 31:167–175
Nemirovski A, Yudin D (1983) Problem complexity and method efficiency in optimization. Wiley, New York
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© 2016 Springer International Publishing Switzerland
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Zaslavski, A.J. (2016). The Mirror Descent Algorithm. In: Numerical Optimization with Computational Errors. Springer Optimization and Its Applications, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-30921-7_3
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DOI: https://doi.org/10.1007/978-3-319-30921-7_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30920-0
Online ISBN: 978-3-319-30921-7
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