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Title: On piecewise quadratic Newton and trust region problems
Authors: Sun, J. 
Keywords: Newton's method
Nonsmooth optimization
Piecewise quadratic programming
Trust region problems
Issue Date: 1997
Citation: Sun, J. (1997). On piecewise quadratic Newton and trust region problems. Mathematical Programming, Series B 76 (3) : 451-467. ScholarBank@NUS Repository.
Abstract: 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.
Source Title: Mathematical Programming, Series B
ISSN: 00255610
Appears in Collections:Staff Publications

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