An Interior-point Algorithm for the Maximum-volume Ellipsoid Problem
نویسنده
چکیده
In this report, we consider the problem of nding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in < n deened by a nite set of aane inequalities. We present several formulations for the problem that may serve as algorithmic frameworks for applying interior-point methods. We propose a practical interior-point algorithm based on one of the formulations and present preliminary numerical results.
منابع مشابه
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...
متن کاملAn infeasible interior-point method for the $P*$-matrix linear complementarity problem based on a trigonometric kernel function with full-Newton step
An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...
متن کاملA path following interior-point algorithm for semidefinite optimization problem based on new kernel function
In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...
متن کاملA 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...
متن کاملConditional Minimum Volume Ellipsoid with Applications to Subset Selection for MVE Estimator and Multiclass Discrimination
In this paper, we present a new formulation for constructing an ellipsoid which generalizes the computation of the minimum volume covering ellipsoid, based on the CVaR minimization technique proposed by Rockafellar and Uryasev (2002). The proposed ellipsoid construction is formulated as a convex optimization and an interior point algorithm for the solution can be developed. In addition, the opt...
متن کامل