6 votes

How to transform this BIP into LP with the help of penalty function?

You can't. If there were a way to transform a MIP to an LP it would mean MIPs can be solved in polynomial time among many other things (edit: not exactly, see below). You can relax the binaries to ...
user avatar
4 votes

How to transform this BIP into LP with the help of penalty function?

If $A$ is totally unimodular, you can replace the binary restrictions on $b$ with $0 \le b_i \le 1$, and solve as an LP. See https://mathoverflow.net/questions/31367/proving-that-a-binary-matrix-is-...
user avatar
3 votes

How to transform this BIP into LP with the help of penalty function?

This might be a candidate for a binary decision diagram (BDD) approach. It involves building a layered digraph. Each layer involves deciding whether a particular variable $b_i$ will be 0 or 1. Each ...
user avatar
  • 31k

Only top scored, non community-wiki answers of a minimum length are eligible