Abstract: "Active set" ideas pervade optimization. In linear programming, for example, we identify active sets with bases. Semidefinite programming has a related notion, involving the rank of slack matrices. Common to the various ideas are two properties, underlying sensitivity theory:

- small changes to the problem do not usually change the optimal "activity ";

- knowing the optimal activity, we can find the optimal solution (locally) simply by solving some smooth equations.

I will try to explain this behaviour by a blend of smooth and nonsmooth optimization theory.