An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
Dual Norm Based Iterative Methods for Image Restoration
Journal of Mathematical Imaging and Vision
Piecewise-quadratic Approximations in Convex Numerical Optimization
SIAM Journal on Optimization
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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We give a proximal bundle method for minimizing a convex function $f$ over a closed convex set. It only requires evaluating $f$ and its subgradients with an accuracy $\epsilon0$, which is fixed but possibly unknown. It asymptotically finds points that are $\epsilon$-optimal. When applied to Lagrangian relaxation, it allows for $\epsilon$-accurate solutions of Lagrangian subproblems and finds $\epsilon$-optimal solutions of convex programs.