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Subgradient Projection Algorithm

In: Convex Optimization with Computational Errors

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  • Alexander Zaslavski

    (Israel Institute of Technology)

Abstract

In this chapter we study the subgradient projection algorithm for minimization of convex and 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 each iteration consists of two steps. The first step is a calculation of a subgradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. 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 steps of our algorithm, we find out what approximate solution can be obtained and how many iterates one needs for this.

Suggested Citation

  • Alexander Zaslavski, 2020. "Subgradient Projection Algorithm," Springer Optimization and Its Applications, in: Convex Optimization with Computational Errors, chapter 0, pages 25-81, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-37822-6_2
    DOI: 10.1007/978-3-030-37822-6_2
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