# Constraint Relaxation

Students of Tai Chi have to grapple with learning how to relax. Its a perennial learning issue for which countless learning methods have been created to help the student learn to relax.

Imagine my surprise on reading the following from this book on algorithms :-

Having determined a problem to be intractable, you can’t just throw up your hands. As a scheduling expert Jan Karel Lenstra told us, “When the problem is hard, it doesn’t mean that you can forget about it, it means that it’s just in a different status. It’s a serious enemy, but you still have to fight it.” And this is where the field figured out something invaluable, something we can all learn from: how to best approach problems whose optimal answers are out of reach. How to relax.

Interesting, right? However, as the authors pointed out when computer scientists try to relax they are not trying to relax themselves. Instead, they relax the problem!

An example of the relaxation approach used in computer science is a method known as Constraint Relaxation. This method calls for the removal of some of the problem’s constraints so that they can set out to solve the problem they wish they had. Then when the simpler problem had been solved they would put back in the removed constraints. The example illustrated in the book is that of the travelling salesman route, a problem I once learned in university as part of Operations Research.

Constraint Relaxation is a method that calls for thought exercises. In Tai Chi we would consider this to be a form of mental simulation of a problem. The typical Tai Chi practitioner might opt to conduct a physical simulation to study a combat problem – whilst this would be easier to do it has certain limitations. A mental simulation would make the investigation a lot easier but it would only work if you have good visualization skills.

Still, in actual practice if we lack the ability to visualize we could still use Constraint Relaxation. Keep in mind that the objective is to make a problem that is difficult to solve solvable. So we have a problem of students grappling with how to relax. The end requirement is the ability to relax the mind and body; we know this is difficult to attain for beginners so we put it aside for the moment. Instead, we focus on what is attainable. What would this be?

You know what, the Tai Chi form is already designed to facilitate learning via Constraint Relaxation. Its just that we don’t have a fancy name for this learning method. To learn to relax we only have to do something simple – practice Raise Hands and Lower Hands over and over again while going through the procedure on how to mobilize the hands in particular paying attention to the feeling, the timing, the placement, etc. Treat it like a minor study and don’t abandon the study half way to try to achieve a big success.

A small achievement is an attainable goal for beginners, those who are patient and prepared to work towards it. I can tell you how to do it, how to go about it, the timelines involved but if the student refuses to listen, is not prepared to let the practice run its course then the objective will forever remain out of reach. As the book’s authors pointed out “The message is simple but profound: if we’re willing to accept solutions that are close enough, then even some of the hairiest problems around can be tamed with the right techniques.

If Constraint Relaxation doesn’t work out for the students, particularly those hard core students who keep insisting on being practical at all times then we could turn to Lagrangian Relaxation. I do fear that these hard core students may lose heart when they realize that having a hard core attitude is not the same as actually being hard core when they discover that the Lagrangian Relaxation method calls for consequences. So if you fail to adhere to the learning rules you might not like the underlying philosophy of “Do it or else you will get it!”

Again, once you get it the intractable learning problem becomes tractable and you have moved a step closer to Master Tai Chi Today. In conclusion, when you can’t relax yourself try relaxing the problem; you could be surprised.

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