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Newton methods for nonsmooth convex minimization: connections among -Lagrangian, Riemannian Newton and SQP methods.
- Source :
-
Mathematical Programming . Oct2005, Vol. 104 Issue 2/3, p609-633. 25p. - Publication Year :
- 2005
-
Abstract
- This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from -Lagrangian theory and from Riemannian geometry. The Hessian based on the -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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 104
- Issue :
- 2/3
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 18632550
- Full Text :
- https://doi.org/10.1007/s10107-005-0631-2