Applications of non-linear kernel Support Vector Machines (SVMs) to large datasets is seriously hampered by its excessive training time. We propose a modification, called the approximate extreme points support vector machine (AESVM), that is aimed at overcoming this burden. Our approach relies on conducting the SVM optimization over a carefully selected subset, called the representative set, of...

The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-po...

We present an efficient algorithm to compute all the extreme elements of a max-plus or tropical polyhedron. This algorithm relies on a combinatorial characterization of these extreme elements, when the polyhedron is defined by inequalities. We show that checking the extremality of an element of such a polyhedron reduces to computing the least model of a compact Horn formula, the latter being a ...

We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present an algorithm with O(n) space and O(nm) time where m is the number of extreme points of P. We also present an algorithm to compute the depth of each point of the given set of n points in d-dimensions. This algorithm has complexity O(n 2) which signiicantly improves the O(n 3) comple...

We describe the central problem in developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints, and discuss a conjecture for its solution.

  We suggest a method for finding the non-dominated points of the production possibility set (PPS) with variable returns to scale (VRS) technology in data envelopment analysis (DEA). We present a multiobjective linear programming (MOLP) problem whose feasible region is the same as the PPS under variable returns to scale for generating non-dominated points. We demonstrate that Pareto solutions o...

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...