A VARIATIONAL APPROACH TO SECOND-ORDER OPTIMALITY

ABSTRATC:

Conditions associated with local optimality, whether necessary or sufficient, have traditionally been approached through techniques of generalized differentiation.  On the first-order level, this has been a long-standing success, although serious challenges remain for equilibrium constraints and the like.   On the second-order level, a difficulty areses with the complex concepts of generalized second derivatives and the sometimes-inadequate calculus for determining them.

In fact, sufficient second-order conditions of a practical sort, which are the most important aid for numerical methodology are largely lacking outside of classical frameworks like nonlinear programming.  In nonlinear programming, well known conditions like so-called strong second-order  optimality are tied to a convexity-concavity property of an augmented Lagrangian function.   It turns out that this pattern can be developed in vastly larger territory by exploiting the recently introduced concept of variational convexity.

 

Date: Nov 20, 2019 at 16:00:00 h
Venue: Beauchef 851, Torre Norte, Piso 7, Sala de Seminarios CMM, John Von Neumann.
Speaker: PROF. TYRRELL ROCKAFELLAR
Affiliation: UNIVERSITY OF WASHINGTON, SEATTLE, USA
Coordinator: Prof. Juan Peypouquet
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Posted on Oct 22, 2019 in Optimization and Equilibrium, Seminars