On bijections that preserve complementarity of subspaces

Transformations on the Product of Grassmann Spaces

Let Gk denote the set of all k-dimensional subspaces of an n-dimensional vector space. We recall that two elements of Gk are called adjacent if their intersection has dimension k − 1. The set Gk is point set of a partial linear space, namely a Grassmann space for 1 < k < n − 1 (see Section 5) and a projective space for k ∈ {1, n − 1}. Two adjacent subspaces are—in the language of partial linear...

An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function

In this paper, an interior-point algorithm  for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...

The Linear Complementarity Problem on Oriented

The linear complementarity problem (LCP) is one of the most widely studied mathematical programming problems. The theory of LCP can be extended to oriented matroids which are combinatorial abstractions of linear subspaces of Euclidean spaces. This paper briefly surveys the LCP, oriented matroids and algorithms for the LCP on oriented matroids. key words: linear complementarity problem, oriented...

Comment on frame's of subspaces

A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...