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3 votes
2 answers
2k views

Formulating a constraint to exclude a single point from the feasible region of an IP?

Consider a basic integer program such as: $$\begin{align} \min_x & \quad c^Tx \\ \text{s.t.} & \quad Ax \leq b \\ &\quad x_i \in \{-100,\ldots,100\} \end{align} $$ where $x \in \mathbb{Z}^n, A \in …
Berk U.'s user avatar
  • 429
0 votes
1 answer
187 views

How to exclude all points adjacent to a given point from the feasible region of IP

Consider a basic integer program such as: $$\begin{align} \min_x & \quad c^Tx \\ \text{s.t.} & \quad Ax \leq b \\ &\quad x_i \in \{-100,\ldots,100\} \end{align} $$ where $x \in \mathbb{Z}^n, A \in …
Berk U.'s user avatar
  • 429
2 votes
3 answers
2k views

Difficulty of Integer Linear Programming vs. Mixed Integer Linear Programming

I have recently been working on an applied project where I have to solve optimization problems. I have found that it is much easier to solve an integer linear program (ILP) as opposed to a mixed-int …
Berk U.'s user avatar
  • 429
1 vote
0 answers
321 views

How to show that an MINLP with L0 regularization is NP-hard?

I am currently working on a project that involves a mixed-integer non-linear optimization problem, and wondering if I can state that this problem NP-hard in a research paper. I'm not looking for a for …
Berk U.'s user avatar
  • 429