Title: Monotone Inclusions and Fitzpatrick Functions
Speaker: Joydeep Dutta, IIT Kanpur
Date and Time: 11:00 am, Tuesday October 13
Venue: Room 217, Mechanical Engineering
Abstract: Fitzpatrick functions are convex functions which represent maximal monotone operators. In this talk we shall see how Fitzpatrick functions can become a gap function for maximal monotone inclusion problems. Since maximal monotone inclusion problems consists of a large class of problems like variational and generalized variational inequalities we also relate the Fitzpatrick function to the known gap functions for these particular classes of problems. We study the notion of a gap of a inclusion problem and this allows us to study complementarity problems in a different way. We will see that we can take a very different view point of looking at the linear programming problem. We will then use the strong Fitzpatrick inequality to talk about the existence of solution to a monotone inclusion and show how an error bound can be developed by looking at the problem from a higher dimension. We also study approximate solutions to the monotone inclusion using the strong Fitzpatrick inequality. We shall the study how a new gap function and error bounds can be developed for a strongly monotone inclusion. (This is joint work with Jonathn. M. Borwein).