Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Hector Sussmann
Affiliation: Rutgers University
Title: Old and new results on optimal curves
Abstract: The talk will first briefly review the classical conditions for optimality of curves due to Euler, Lagrange, Legendre, Hamilton, and Weierstrass, emphasizing some interesting "missed opportunities" stories, where dramatic progress would have been possible if only the Hamilton equations had been written "correctly" ab initio. After this introduction, we will move on to the relatively newer perspective provided by the Pontryagin Maximum Principle in the 1950s, by nonsmooth techniques in the 1970s, and by some recent results on nonsmooth and high-order conditions based on transversal intersection theorems for general sets. We will conclude with a somewhat pessimistic assessment of the the possibility that a truly unified approach might emerge, but with a second-best suggestion that there probably are exactly two approaches ("limiting" and "fixed point") thar are technically different and cannot be combined into a single one, but are both based on the unifying idea of transversality of cones and multicones. The pessimistic conclusion will be justified by appealing to a counterexample discovered by A. Bressan in January 2006, while the optimistic "second-best idea" will be supported by recent work of ours on the Lipschtiz maximum principle.
