Gradient Algorithm with a Smooth Objective Function

Alexander J. Zaslavski
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Alexander J. Zaslavski: The Technion – Israel Institute of Technology

Chapter Chapter 4 in Numerical Optimization with Computational Errors, 2016, pp 59-72 from Springer

Abstract: Abstract In this chapter we analyze the convergence of a projected gradient algorithm with a smooth objective function under the presence of computational errors. We show that the algorithm generates 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.

Keywords: Hilbert Space; Approximate Solution; Convex Subset; Gradient Algorithm; Nonempty Closed Convex Subset (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30921-7_4

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DOI: 10.1007/978-3-319-30921-7_4

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