Krzysztof C. Kiwiel

Inexact Dynamic Bundle Methods

  • Krzysztof C. Kiwiel
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    We give a proximal bundle method for minimizing a convex function $f$ over $\mathbb{R}_+^n$. It requires evaluating $f$ and its subgradients with a possibly unknown accuracy $\epsilon\ge0$, and maintains a set of free variables $I$ to simplify its prox subproblems. The method asymptotically finds points that are $\epsilon$-optimal. In Lagrangian relaxation of convex programs, it … Read more

    Bundle Methods for Convex Minimization with Partially Inexact Oracles

  • Krzysztof C. Kiwiel
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Recently the proximal bundle method for minimizing a convex function has been extended to an inexact oracle that delivers function and subgradient values of unknown accuracy. We adapt this method to a partially inexact oracle that becomes exact only when an objective target level for a descent step is met. In Lagrangian relaxation, such oracles … Read more