Title: Conditioning of Optimization Problems



			  Asen L. Dontchev
   		     AMS, Mathematical Reviews
   			 416 Fourth Street
   		      Ann Arbor, MI 48107-8604
   			     ald@ams.org
	    

Abstract:
Concepts of conditioning have long been important in numerical work
on solving systems of equations, but in recent years attempts have been
made to extend them to feasibility conditions, optimality conditions,
complementarity conditions and variational inequalities, all of which
can be posed as solving ``generalized equations'' for set-valued mappings.
In the talk, the conditioning of such generalized equations is systematically
organized around four key notions: metric regularity, subregularity,
strong regularity and strong subregularity.  Various properties and
characterizations already known for metric regularity itself are extended
to strong regularity and strong subregularity, but metric subregularity,
although widely considered, is shown to be too fragile to support stability
results such as a radius of good behavior modeled on the Eckart-Young
theorem.