B. Curtis Eaves

Homotopies for computation of fixed points

Given a point to set mapf on a simplex with certain conditions, an algorithm for computing fixed points is described. The algorithm operates by following the fixed point as an initially affine function is deformed towardsf.

Homotopies for computation of fixed points on unbounded regions

Givenf: Rn→ Rn* with some conditions, our aim is to compute a fixed pointx ∈ f(x) off; hereRn isn-dimensional Euclidean space andRn* is the collection of nonempty subsets ofRn. A typical application of the algorithm can be motivated as follows: Beginning with the constant mapf0:Rn → {0} ⊂Rn and its fixed pointx0 = 0, we deformft ast → ∞ tof∞∈ f and follow the pathxt of fixed points offt. Cluster points of thexts ast → ∞ are fixed points off.

Generalized Cutting Plane Algorithms

This paper introduces a master cutting plane algorithm for nonlinear programming that isolates the points it generates from one another until a solution is achieved. The master algorithm provides a foundation for the study of cutting plane algorithms and directs the way for development of procedures which permit deletion of old cuts.

A finite algorithm for the linear exchange model

It is shown that Lemkes algorithm can be used to compute, in a finite number of steps, an equilibrium or reduction for the pure exchange model with linear utilities.

Computing Kakutani Fixed Points

Let C be a compact convex subset of

Computing Economic Equilibria on Affine Networks with Lemke's Algorithm

R^m

Homotopy methods and global convergence

, let

A course in triangulations for solving equations with deformations

C^ *

Polymatrix Games with Joint Constraints

be the set of compact convex subsets of C, and let

Optimal scaling of balls and polyhedra

f:C \to C^ *