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The Newton Bracketing Method for Convex Minimization: Convergence Analysis

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Adi Ben-Israel

    (Rutgers University)

  • Yuri Levin

Abstract

Let f be a convex function bounded below with infimum f min attained. A bracket is an interval [L, U] containing f min. The Newton Bracketing (NB) method for minimizing f, introduced in [Levin and Ben-Israel, Comput. Optimiz. Appl. 21, 213–229 (2002)], is an iterative method that at each iteration transforms a bracket [L, U] into a strictly smaller bracket $$[{L}_{+},{U}_{+}]$$ with $$L \leq {L}_{+}

Suggested Citation

  • Adi Ben-Israel & Yuri Levin, 2011. "The Newton Bracketing Method for Convex Minimization: Convergence Analysis," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 49-64, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_4
    DOI: 10.1007/978-1-4419-9569-8_4
    as

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