Monday, January 29, 2007.
4:15 PM.
Location: Bldg 380, Room 380C (basement)
Refreshments served at 4:00PM in the courtyard outside Room 380C
In this talk I will give an overview of general convex
optimization,
which can be thought of as an extension of linear programming,
and some recently developed subfamilies such as second-order cone,
semidefinite, and geometric programming. Like linear programming,
we have a fairly complete duality theory, and
very effective numerical methods for these problem classes;
in addition, recently developed software tools considerably
reduce the effort of specifying and solving convex optimization
problems.
There is a steadily expanding list of new applications of convex
optimization, in areas such as circuit design, signal processing,
statistics, machine learning, communications, control, finance,
and other fields. Convex optimization is also emerging as an
important tool for hard, non-convex problems, where it can be used to
generate lower bounds on the optimal value, and as a heuristic method