The Newton Bracketing Method for Convex Minimization: Convergence Analysis

Adi Ben-Israel () and Yuri Levin
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Adi Ben-Israel: Rutgers University

Chapter Chapter 4 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 49-64 from Springer

Abstract: 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}_{+}

Keywords: Newton Bracketing method; Directional Newton method; Convex functions; Unconstrained minimization; Fermat–Weber location problem (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-9569-8_4

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