May 23, 2001 from 10:30-12:00 in K9509, SFU
Adrian Lewis, SFu
"ACTIVE SETS IN OPTIMIZATION"
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.