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|Title:||On piecewise quadratic Newton and trust region problems|
Piecewise quadratic programming
Trust region problems
|Source:||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|
|Appears in Collections:||Staff Publications|
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