Abstract
In this chapter we study the continuous subgradient algorithm for minimization of convex nonsmooth functions and for computing the saddle points of convex–concave functions, under the presence of computational errors. The problem is described by an objective function and a set of feasible points. For this algorithm we need a calculation of a subgradient of the objective function and a calculation of a projection on the feasible set. In each of these two calculations there is a computational error produced by our computer system. In general, these two computational errors are different. We show that our algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if we know the computational errors for the two calculations of our algorithm, we find out what approximate solution can be obtained and how much time one needs for this.
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J. Zaslavski, A. (2020). Continuous Subgradient Method. In: Convex Optimization with Computational Errors. Springer Optimization and Its Applications, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-030-37822-6_6
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DOI: https://doi.org/10.1007/978-3-030-37822-6_6
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