Mathematical Programming

, Volume 104, Issue 2, pp 609–633

Newton methods for nonsmooth convex minimization: connections among, Riemannian Newton and SQP methods


DOI: 10.1007/s10107-005-0631-2

Cite this article as:
Miller, S. & Malick, J. Math. Program. (2005) 104: 609. doi:10.1007/s10107-005-0631-2


This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from theory and from Riemannian geometry. The Hessian based on the depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for which the two Newton directions coincide. This choice of g is also shown to be related to the least-squares multiplier estimate from a sequential quadratic programming (SQP) approach, and with this multiplier, SQP gives the same search direction as the Newton methods.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Numerica Corp.Ft. CollinsUSA
  2. 2.INRIASaint Ismier CedexFrance