Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Nondifferentiable optimization
Optimization
Approximations in proximal bundle methods and decomposition of convex programs
Journal of Optimization Theory and Applications
A quasi-second-order proximal bundle algorithm.
Mathematical Programming: Series A and B
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
An approximate decomposition algorithm for convex minimization
Journal of Computational and Applied Mathematics
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
Level bundle methods for constrained convex optimization with various oracles
Computational Optimization and Applications
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In this paper a proximal bundle method is introduced that is capable to deal with approximate subgradients. No further knowledge of the approximation quality (like explicit knowledge or controllability of error bounds) is required for proving convergence. It is shown that every accumulation point of the sequence of iterates generated by the proposed algorithm is a well-defined approximate solution of the exact minimization problem. In the case of exact subgradients the algorithm behaves like well-established proximal bundle methods. Numerical tests emphasize the theoretical findings.