Convex optimization cheat sheet

How do you solve a convex optimization problem?

There is in general no analytical formula for the solution of convex optimization problems, but (as with linear programming problems) there are very effective meth- odsfor solvingthem

Interior-pointmethods workverywell in practice, and in some cases can be proved to solve the problem to a specified accuracy with a number of

What is the optimal set if the objective is convex?

In particular, the optimal set is convex

If the objective is strictly convex, then the optimal set contains at most one point

Concave maximization problems With a slight abuse of notation, we will also refer to maximize f


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