Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/26039
Title: The lagrangian globalization method for nonsmooth constrained equations
Authors: Tong, X
Qi, L 
Yang, YF
Keywords: Constrained nonsmooth equations
Global convergence
Lagrangian globalization method
Stationary point
Issue Date: 2006
Publisher: Springer
Source: Computational optimization and applications, 2006, v. 33, no. 1, p. 89-109 How to cite?
Journal: Computational optimization and applications 
Abstract: The difficulty suffered in optimization-based algorithms for the solution of nonlinear equations lies in that the traditional methods for solving the optimization problem have been mainly concerned with finding a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. One method to overcome this difficulty is the Lagrangian globalization (LG for simplicity) method. This paper extends the LG method to nonsmooth equations with bound constraints. The absolute system of equations is introduced. A so-called Projected Generalized-Gradient Direction (PGGD) is constructed and proved to be a descent direction of the reformulated nonsmooth optimization problem. This projected approach keeps the feasibility of the iterates. The convergence of the new algorithm is established by specializing the PGGD. Numerical tests are given.
URI: http://hdl.handle.net/10397/26039
ISSN: 0926-6003
EISSN: 1573-2894
DOI: 10.1007/s10589-005-5960-9
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