Abstract
Methods for minimization of composite functions with a nondifferentiable polyhedral convex part are considered. This class includes problems involving minimax functions and norms. Local convergence results are given for “active set” methods, in which an equality-constrained quadratic programming subproblem is solved at each iteration. The active set consists of components of the polyhedral convex function which are active or near-active at the current iteration. The effects of solving the subproblem inexactly at each iteration are discussed; rate-of-convergence results which depend on the degree of inexactness are given.
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Wright, S.J. Local properties of inexact methods for minimizing nonsmooth composite functions. Mathematical Programming 37, 232–252 (1987). https://doi.org/10.1007/BF02591697
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DOI: https://doi.org/10.1007/BF02591697