Farid Alizadeh The minimum $k$-enclosing ball problem seeks the ball with smallest radius that contains at least $k$ of $m$ given points in a general $n$-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of $k$ points to solve this problem. The nodes on the tree are ordered … Read more
Dearing and Zeck presented a dual algorithm for the problem of the minimum covering ball in $\mathbb{R}^n$. Each iteration of their algorithm has a computational complexity of at least $\mathcal O(n^3)$. In this paper we propose a modification to their algorithm that, together with an implementation that uses updates to the QR factorization of a … Read more
This paper approximates simulation models by B-splines with a penalty on high-order finite differences of the coefficients of adjacent B-splines. The penalty prevents overfitting. The simulation output is assumed to be nonnegative. The nonnegative spline simulation metamodel is casted as a second-order cone programming model, which can be solved efficiently by modern optimization techniques. The … Read more
We extend Nesterov’s semidefinite programming (SDP) characterization of the cone of functions that can be expressed as sums of squares (SOS) of functions in finite dimensional linear functional spaces. Our extension is to algebraic systems that are endowed with a binary operation which map two elements of a finite dimensional vector space to another vector … Read more
Based on the Q method for SDP, we develop the Q method for SOCP. A modified Q method is also introduced. Properties of the algorithms are discussed. Convergence proofs are given. Finally, we present numerical results. CitationAdvOl-Report#2004/15 McMaster University, Advanced Optimization LaboratoryArticleDownload View PDF
We extend the Q method to the symmetric cone programming. An infeasible interior point algorithm and a Newton-type algorithm are given. We give convergence results of the interior point algorithm and prove that the Newton-type algorithm is good for CitationAdvOl-Report#2004/18 McMaster University, Advanced Optimization Laboratory Hamilton, Ontario, Canada October 2004ArticleDownload View PDF