Removing Equality Constraints

Learn to solve optimization problems with equality constraints.

We’re going to learn about good constraints. Those are constraints that make our lives easier.

Getting started with equality constraints

Remember the problem of finding the smaller surface of the soda cans? Here’s the problem formulation:

minr,h2πrh+2πr2s.t.:πr2h=355\min_{r, h} 2\pi rh + 2\pi r^2 \\ s.t.: \pi r^2h = 355

That constraint was helpful. We knew how to deal with the target functions of one variable and the constraint helped us to get rid of variable hh.

We used the constraint to make hh a function of rr:

h=355πr2h = \frac{355}{\pi r^2}

Then we transformed the target function accordingly:

minr2πr355πr2+2πr2\min_{r} 2\pi r\frac{355}{\pi r^2} + 2\pi r^2

We transformed a multivariate constrained problem into a univariate unconstrained one. A pretty good deal!

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