In this paper we analyze the parallel approximability of two special classes of Quadratic Programming. First, we consider Convex Quadratic Programming. We show that the problem of Approximating Convex Quadratic Programming is P-complete. We also consider two approximation problems related to it, Solution Approximation and Value Approximation and show both of these cannot be solved in NC, unless...

We introduce a novel representation of classifier conditions based on convex hulls. A classifier condition is represented by a sets of points in the problem space. These points identify a convex hull that delineates a convex region of the problem space. The condition matches all the problem instances inside such region. We apply XCSF with convex conditions to function approximation problems and...

Subset selection and sparse approximation problems request a good approximation of an input signal using a linear combination of elementary signals, yet they stipulate that the approximation may only involve a few of the elementary signals. This class of problems arises throughout electrical engineering, applied mathematics and statistics, but small theoretical progress has been made over the l...

Finding minimum triangulations of convex 3-polytopes is NP-hard. The best approximation algorithms only give an approximation ratio of 2 for this problem, which is the best possible asymptotically when only combinatorial structures of the polytopes are considered. In this paper we improve the approximation ratio of finding minimum triangulations for some special classes of 3-dimensional convex ...

In this paper, we study two classic optimization problems: minimum geometric dominating set and set cover. In the dominating set problem, for a given set of objects as input, the objective is to choose minimum number of input objects such that every input object is dominated by the chosen set of objects. Here, one object is dominated by the other if both of them have non-empty intersection regi...

We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same Hessia...

A new technique for polytope approximation of the feasible region for a design is presented. This method is computationally less expensive than the simplicial approximation method [1]. Results on several circuits are presented, and it is shown that the quality of the polytope approximation is substantially better than an ellipsoidal approximation.

This paper deals with sparse approximations by means of convex combinations of elements from a predetermined \basis" subset S of a function space. Speciically, the focus is on the rate at which the lowest achievable error can be reduced as larger subsets of S are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron, including in par...

Assume K ⊂ R is a convex body and Xn ⊂ K is a random sample of n uniform, independent points from K. The convex hull of Xn is a convex polytope Kn called random polytope inscribed in K. We are going to investigate various properties of this polytope: for instance how well it approximates K, or how many vertices and facets it has. It turns out that Kn is very close to the so called floating body...