Questions tagged [valid-inequalities]

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5
votes
1answer
107 views

Guidelines for adding user cuts to models

Given that you have identified a new class of valid inequalities. What are some guidelines on when and how many and which of the violated user cuts you add to the model? I know that this involves a ...
10
votes
3answers
210 views

Is the “reverse search” algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities?

Is the "reverse search" algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities? If it is not, then what is? For $m$ inequalities in $d$ ...
9
votes
2answers
297 views

Valid Inequalities and Strong Inequalities

Consider the following mixed-integer set: \begin{equation} P(A, b ; S) \stackrel{\text { def }}{=}\left\{x \in \mathbb{R}^{n} : A x \leq b, x_{j} \in \mathbb{Z} \text { for } j \in S\right\} \end{...
14
votes
2answers
770 views

State-of-the-art algorithms for solving linear programs

Průša and Werner (2019) show that the general linear programming problem reduces in nearly linear time to the LP relaxations of many classical NP-hard problems (assuming sparse encoding of instances)....
11
votes
1answer
136 views

How to relate dual values of valid inequality to the dual values of the original problem?

I have a given formulation that looks like this (just for the constraints): $$\sum_i \beta_{i,j} \geq \alpha_j,\qquad\forall j$$ $$\alpha_j \geq \sum_i f_{i,j},\qquad\forall j$$ $$\alpha_j \geq 0, ...
21
votes
3answers
1k views

Are valid inequalities worth the effort given modern solvers?

In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also ...