MASSACHUSETTS INSTITUTE OF TECHNOLOGY
OPERATIONS RESEARCH CENTER
FALL 2004 SEMINAR SERIES

DATE

Thursday, October 21, 2004

LOCATION: Room E40-298           TIME: 4:15pm

Reception immediately following in the
Philip M. Morse Reading Room, E40-106

SPEAKER

Professor Dimitri Bertsekas
McAfee Professor of Engineering
Lab. for Information and Decision Systems
MIT

TITLE

Fritz John Multipliers with Sensitivity Properties

ABSTRACT

     We consider convex constrained optimization problems, and we enhance the classical Fritz John optimality conditions to assert the existence of multipliers with special sensitivity properties. In particular, we prove the existence of Fritz John multipliers that are informative in the sense that they identify constraints whose relaxation, at rates proportional to the multipliers, strictly improves the primal optimal value.

     Moreover, we show that if the set of Lagrange multipliers is nonempty, then the minimum-norm vector of this set is informative, and defines the optimal rate of cost improvement per unit constraint violation. Our assumptions are very general, and allow for the presence of duality gap and the non-existence of optimal solutions. In particular, for the case where there is a duality gap, we establish enhanced Fritz John conditions involving the dual optimal value and dual optimal solutions.