Invited Session Mon.3.MA 041

Monday, 15:15 - 16:45 h, Room: MA 041

Cluster 3: Complementarity & variational inequalities [...]

Analysis and learning in variational inequalities


Chair: Shu Lu



Monday, 15:15 - 15:40 h, Room: MA 041, Talk 1

Hao Jiang
Learning parameters and equilibria in noise-corrupted Cournot games with misspecified price functions

Coauthors: Sean Meyn, Uday Shanbhag


We consider an oligopolistic setting in which myopic firms compete in a repeated Nash-Cournot game. In accordance with the Cournot assumption, prices are set based on aggregate output levels. We develop distributed learning schemes in a regime where firms are ignorant of a complete specification of an affine price function; specifically, firms learn the equilibrium strategy and correct the misspecification in the price function by simultaneously incorporating noise-corrupted observations and demand function. Differentiated by informational assumptions, two sets of schemes are developed and their performance is demonstrated on a networked Nash-Cournot game:
(1) Learning under common knowledge with unobservable aggregate output: Here, payoff
functions and strategy sets are public knowledge (a common knowledge assumption) but aggregate output is unobservable. When firms may observe noise-corrupted prices, distributed best response schemes are developed which allow for simultaneously learning the equilibrium strategy and the misspecified parameter in an almost-sure sense. Furthermore, these statements may be extended to accommodate nonlinear generalizations of the demand function.



Monday, 15:45 - 16:10 h, Room: MA 041, Talk 2

Stephen Michael Robinson
Local analysis of variational conditions


We will present a mathematical framework for local analysis of variational conditions in finite-dimensional spaces, and will illustrate some of its applications. We will also illustrate some forms of the fundamental regularity conditions for this analysis, and discuss connections among these.



Monday, 16:15 - 16:40 h, Room: MA 041, Talk 3

Andreas Fischer
A framework for smooth and nonsmooth equations with nonisolated solutions

Coauthors: Francisco Facchinei, Markus Herrich


The problem of solving a system of possibly nonsmooth equations appears in
several applications. For example, complementarity problems or
Karush-Kuhn-Tucker conditions of an inequality constrained
optimization problem
can be written in this way. A new local iterative framework for solving
systems of equations under additional convex constraints will be presented.
In particular, the framework includes conditions for local superlinear
convergence. These conditions enable the application to nonsmooth systems
nonisolated solutions. Different algorithms belonging to the framework will
be described.


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