The most basic issue in economic equibrium, concerning the exchange of goods by agents through a market, can be modeled as a variational inequality problem with the initial supplies of goods as parameters. The question arises then as to how the equilibrium prices and goods respond to shifts in those parameters. Results of variational analysis...

# Videos

## The Australian Mathematical Science Institute and the IRMACS Centre Present:

A Workshop on Computational and Analytical Mathematics - Video Recordings

Luke, Russel

Many problems of interest where more than one solution is possible seek, among these, the one that is sparsest. The objective that most directly accounts for sparsity, the *TeX Embedding failed!* metric, is usually avoided since this leads to a combinatorial optimization problem. The function *TeX Embedding...*

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Wang, Shawn

Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. We give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional spaces. Our results generalize a recent result by Crouzeix and Anaya.

Dontchev, Asen L.

We study convergence of inexact Newton methods for solving variational inequalities. First, we consider an extension of the method proposed by Dembo, Eisenstat, and Steihaug for solving equations. We show how regularity properties of the the mapping involved in the variational inequality are able to guarantee that every sequence generated...

Beer, Gerald

We show that the weak Ekeland variational principle is itself derivative of a geometric principle for Lipschitz real-valued functions. We use this principle to directly obtain an omnibus result regarding the nonempty intersection of a decreasing sequence of nonempty closed sets. Both the weak Ekeland principle and our principle for Lipschitz...