# Tag Info

### Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?

It's not exactly the same thing, but very close: in goal programming, using a weighted combination of the deviations from goals is often called "Archimedean" (as in "Archimedean" goal programming, or ...

### Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?

The act of moving soft constraint into the objective function using penalties is closely related to Lagrangian Relaxation and Lagrangian Multipliers. The method penalizes violations of [...] ...

### 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 ...
Accepted

### Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

This problem is addressed in some detail in Section 2.1 of the paper Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems by Watson and Woodruff (a non-...

### Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?

I’m not sure I’ve heard a canonical name, but that sounds like a multi-objective optimization problem where you’re minimizing the sum of weighted deviations. The weights are based on the constraint ...

### Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?

One common way I've seen in the literature to deal with such cases is to multiply the priority constraint by a big weight and add it into the fitness function alongside the lower priority constraint. ...

### 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-...
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 ...