On piecewise quadratic Newton and trust region problems |
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Authors: | J Sun |
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Institution: | (1) Department of Decision Sciences, National University of Singapore, 119260 Singapore |
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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.
Partially supported by National University of Singapore under grant 930033. |
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Keywords: | Newton’ s method Nonsmooth optimization Piecewise quadratic programming Trust region problems |
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