An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
Piecewise-quadratic Approximations in Convex Numerical Optimization
SIAM Journal on Optimization
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We give a proximal bundle method for minimizing a convex function $f$ over a convex set $C$. It requires evaluating $f$ and its subgradients with a fixed but possibly unknown accuracy $\epsilon0$. Each iteration involves solving an unconstrained proximal subproblem and projecting a certain point onto $C$. The method asymptotically finds points that are $\epsilon$-optimal. In Lagrangian relaxation of convex programs, it allows for &egr;-accurate solutions of Lagrangian subproblems and finds &egr;-optimal primal solutions. For semidefinite programming problems, it extends the highly successful spectral bundle method to the case of inexact eigenvalue computations.