Weighted LCPs and interior point systems for copositive linear transformations on Euclidean Jordan algebras

In the setting of a Euclidean Jordan algebra V with symmetric cone V_+, corresponding to a linear transformation M, a `weight vector’ w in V_+, and a q in V, we consider the weighted linear complementarity problem wLCP(M,w,q) and (when w is in the interior of V_+) the interior point system IPS(M,w,q). When M is … Read more

Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones

Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map f:C–>H is a sum of two continuous maps h and g, where h is positively homogeneous of (positive) degree gamma on C and g(x)/||x||^gamma–>0 as ||x||–>infinity in C. Given such a map f, a nonempty closed convex … Read more

The central curve in linear programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal … Read more