Abstract
Putting a finer structure on a constraint matrix than is afforded by subdeterminant bounds, we give sharpened proximity results for the setting of k-regular mixed-integer linear optimization.
Supported in part by ONR grant N00014-17-1-2296.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aliev, I., Henk, M., Oertel, T.: Distances to lattice points in knapsack polyhedra. arXiv preprint arXiv:1805.04592 (2018)
Cook, W., Gerards, A.M., Schrijver, A., Tardos, É.: Sensitivity theorems in integer linear programming. Math. Program. 34(3), 251–264 (1986)
Eisenbrand, F., Weismantel, R.: Proximity results and faster algorithms for integer programming using the Steinitz lemma. In: SODA. pp. 808–816 (2018)
Granot, F., Skorin-Kapov, J.: Some proximity and sensitivity results in quadratic integer programming. Math. Program. 47(1–3), 259–268 (1990)
Hochbaum, D.S., Shanthikumar, J.G.: Convex separable optimization is not much harder than linear optimization. J. ACM 37(4), 843–862 (1990)
Lee, J.: Subspaces with well-scaled frames. Ph.D. dissertation, Cornell University (1986)
Lee, J.: Subspaces with well-scaled frames. Linear Algebra Appl. 114, 21–56 (1989)
Lee, J.: The incidence structure of subspaces with well-scaled frames. J. Comb. Theory Ser. B 50(2), 265–287 (1990)
Paat, J., Weismantel, R., Weltge, S.: Distances between optimal solutions of mixed-integer programs. Math. Program. https://doi.org/10.1007/s10107-018-1323-z (2018)
Rockafellar, R.T.: The elementary vectors of a subspace of \({\mathbb{R}}^n\). In: Combinatorial Mathematics and Its Applications, pp. 104–127. University of North Carolina Press (1969)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley (1998)
Veselov, S.I., Chirkov, A.J.: Integer program with bimodular matrix. Discrete Optim. 6(2), 220–222 (2009)
Werman, M., Magagnosc, D.: The relationship between integer and real solutions of constrained convex programming. Math. Prog. 51(1), 133–135 (1991)
Zaslavsky, T.: Signed graphs. Discrete Appl. Math. 4(1), 47–74 (1982)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Xu, L., Lee, J. (2020). On Proximity for k-Regular Mixed-Integer Linear Optimization. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_44
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_44
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)