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2797. Decomposition, Cutting Planes and Column Generation with Interior Point Methods

Invited abstract in session MC-30: Continuous Solvers, stream Software for Optimization.

Monday, 12:30-14:00
Room: 064 (building: 208)

Authors (first author is the speaker)

1. Jacek Gondzio
School of Mathematics, University of Edinburgh

Abstract

In this talk we shall explain the reasons why interior point methods
(IPMs) deliver particularly attractive features when they are applied
in the context of decomposition methods, cutting plane schemes
and column generation techniques.
These features include:
(1) generating epsilon-subgradients in Benders and Dantzig-Wolfe decomposition,
(2) finding (stable) well-centred solutions of restricted master problems,
(3) delivering on-demand accuracy in column generation.
It goes without saying that these features cannot be delivered
by the simplex-based solvers.
Some of the advantages will be illustrated when solving
very large discrete optimal transport problems.

References:
J.Gondzio,
Interior Point Methods in the Year 2024,
Technical Report, February 28, 2024.
Submitted for publication.

Keywords

Status: accepted

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