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An update-and-stabilize framework for the minimum-norm-point problem

Fujishige, Satoru, Kitahara, Tomonari and Végh, László A. ORCID: 0000-0003-1152-200X (2023) An update-and-stabilize framework for the minimum-norm-point problem. In: Del Pia, Alberto and Kaibel, Volker, (eds.) Integer Programming and Combinatorial Optimization - 24th International Conference, IPCO 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Science and Business Media Deutschland GmbH, pp. 142-156. ISBN 9783031327254

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Identification Number: 10.1007/978-3-031-32726-1_11


We consider the minimum-norm-point (MNP) problem of polyhedra, a well-studied problem that encompasses linear programming. Inspired by Wolfe’s classical MNP algorithm, we present a general algorithmic framework that performs first order update steps, combined with iterations that aim to ‘stabilize’ the current iterate with additional projections, i.e., finding a locally optimal solution whilst keeping the current tight inequalities. We bound the number of iterations polynomially in the dimension and in the associated circuit imbalance measure. In particular, the algorithm is strongly polynomial for network flow instances. The conic version of Wolfe’s algorithm is a special instantiation of our framework; as a consequence, we obtain convergence bounds for this algorithm. Our preliminary computational experiments show a significant improvement over standard first-order methods.

Item Type: Book Section
Additional Information: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics
Date Deposited: 28 Jul 2023 10:18
Last Modified: 09 Jun 2024 16:03

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