Mathematical Programming

, Volume 104, Issue 2–3, pp 609–633 | Cite as

Newton methods for nonsmooth convex minimization: connections among Open image in new window-Lagrangian, Riemannian Newton and SQP methods



This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from Open image in new window-Lagrangian theory and from Riemannian geometry. The Hessian based on the Open image in new window-Lagrangian 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.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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

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