What does relaxing constraints mean?

Pretty technical, but I think it fits

In college I took a course called Linear Programming. You use it to optimize all sorts of things such as maximizing profits subject to sets of constraints. A constraint is essentially a rule that has to be followed. If you are running a warehouse, some constraints could be a person can work up to 8 hours and carry up to 10 items and 40 pounds at a time. However, not all problems are easy to find a solution to and in those cases we sometimes have to relax a constraint to find a solution. In the warehouse example a person would only carry a discrete number of items, you can’t carry half an item. However, no efficient algorithm exists to solve this problem. So we relax the whole number (integrality) constraint and let it be anything from 0 to 1. For that there exists an algorithm and you can choose a whole number close to the solution. The image below is an example where there are three constraints. If you are trying to maximize y, the solution is (1,3). I thought it would be funny to have a character relaxing on a constraint, so I hired an artist to create this. Now you understand the meaning behind the name and what my logo is.

Can you use linear programming to optimize your life? Probably not in a way that can be solved by an algorithm, but we can apply the concepts. Your life is something which may have an optimal point, but you’ll never know exactly where it is. We can try different things that are within our abilities and evaluate the outcomes. You’ll probably be able to tell when you are heading in the right direction.

Our constraints

We too live by a multitude of constraints. Here are some examples: keep your heart pumping, eat 3 meals a day, drive the speed limit, sleep 8 hours, spend less than our credit limit. These constraints limit our behavior to a set of possible actions. You can’t go buy a yacht tomorrow because you are constrained by they amount of money you have. You go to work everyday because your employer has set that expectation and you want to keep your job.

Constraints can come from many places. Some are a due to our environment. Even if you wanted to jump 20 feet high the laws of physics are going to stop you. Other constraints come from our body. You need breath, eat, and sleep or you’ll die. Often, you will impose constraints on yourself. When you get married you are constraining yourself to your spouse. Society throws a bunch of constraints at us as well often codified in law. You can’t shoplift or drive under the influence. It’s not illegal, but you wouldn’t sneeze on someone. Constraints can also come from others. Your employer probably has rules which limit your behavior. If you start disparaging your employer online it probably wouldn’t be long before you are let go.

Constraints aren’t necessarily bad or good, but they limit what you can do. Sometimes we feel our constraints are too tight, but there’s good news because it is possible to change your set of constraints.

Relaxing constraints

Some constraints are firmer than others. No matter how much you want to, you can’t relax the laws of physics or your body’s requirements. Meanwhile, following the speed limit is a constraint that drivers are relaxing all the time. When we relax a constraint it is often at the cost of something else. Instead of going to bed on time to sleep 8 hours, you relax that constraint so you can watch another Netflix episode. You may decide to relax the constraint of being without credit card debt so you can take a trip to Europe. Trade-offs and opportunity costs are closely related to constraints, but that’s for another article.

When you decide to relax a constraint it’s because you, perhaps unconsciously, deem something more important and are willing to relax your constraints to get it done. Sometimes the cost is negligible while other times it can cost you everything. Figuring out what is worth it is up to you, but there should be thought that goes into the decision.

Constraints I have relaxed

It may be helpful if I provide some of the larger examples from my life where I needed to relax a constraint.

One constraint I put on myself was the need to retire by age 40. I was a big follower of Mr. Money Mustache and thought the optimal lifestyle would be frugality until financial independence when I could live as I pleased. However, this lifestyle would mean not traveling much while I was young and healthy. I decided it would be better to work longer while building memories exploring rather than simply trying to finish work.

We used to live in Irvine, one of the safest cities in America. But it’s not the most exciting place. At some point, we decided that it was constraint on our happiness. We decided to move away and that lead us to Lisbon where we spent a wonderful year.

The pandemic put new constraints on everyone. Now you were confined to your home, had to wear a mask, and still had to go to work. Many had the seemingly impossible constraints of watching children while simultaneously working. We decided to relax the constraint of staying put without help and split our time between parents in California and Texas. We rented out the house since we weren’t using it much.

Identify Your Constraints

Now that you have an understanding of constraints, the next step is to identify your constraints. By identifying them it will be easier to understand why you can’t do something or what you’d need to relax in order to accomplish it. And I’m guessing there are many things you would like to accomplish but haven’t found the time, money, or effort to get around to it. In future articles I’ll share next steps of how we can go about choosing which of our constraints to keep, relax, or discard.