On piecewise quadratic Newton and trust region problems

Data:	1997
Resum:	Some recent algorithms for nonsmooth optimization require solutions to certain piecewise quadratic programming subproblems. Two types of subproblems are considered in this paper. The first type seeks the minimization of a continuously differentiable and strictly convex piecewise quadratic function subject to linear equality constraints. We prove that a nonsmooth version of Newton's method is globally and finitely convergent in this case. The second type involves the minimization of a possibly nonconvex and nondifferentiable piecewise quadratic function over a Euclidean ball. Characterizations of the global minimizer are studied under various conditions. The results extend a classical result on the trust region problem. .
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Newton's method ; Nonsmooth optimization ; Piecewise quadratic programming ; Trust region problems
Publicat a:	Mathematical Programming, vol. 76 n. 3 (1997) p. 451-467, ISSN 0025-5610

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