Integer Program Combination Optimization - Problem Set 1 - Edubirdie

University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

93

Pages:

2
Author:

Jamarion Zamora

Integer Optimization Assignment 1 Exercises from BW 1.7, 1.9, 1.11, 1.20, 2.1, 2.5, 2.10. 1 Exercise 2.10 (modiﬁed) Let G = (V, E) be an undirected graph. Let C = {1, 2, . . . , 2k + 1} ⊆ V be a cycle of odd cardinality, such that there are no edges {i, j} for j = i + 1. Let h be a node such that {i, h} ∈ E for all i ∈ C. Use the method of disjunctions to show that the inequality � i∈C xi + |C| − 1 |C| − 1 xh ≤ 2 2 is valid for the convex hull of stable sets in G. Is this inequality facet deﬁning? 1

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