An interior-point method for the single-facility location problem with mixed norms using a conic formulation

We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R, where each distance can be measured according to a different p-norm.We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.nonsymmetric conic optimization, conic reformulation, convex optimization, sum of norm minimization, single-facility location problems, interior-point methods

An interior-point method for the single-facility location problem with mixed norms using a conic formulation

Abstract We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R n , where each distance can be measured according to a different p-norm. We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem

Cones and interior-point algorithms for structured convex optimization involving powers andexponentials

Optimization is an important field of applied mathematics with many applications in various domains, ranging from mechanical and electrical engineering to finance and operations research. In particular, convex optimization is very popular because of the availability of highly efficient methods supported by strong theoretical results. In this thesis, we study interior-point methods whose computing time is guaranteed to grow polynomially with the problem dimension. These methods can be applied to any convex problem provided a special function known as a self-concordant barrier is available for the given formulation. We demonstrate in this work that a large class of convex optimization problems are representable in a convex conic form based on the so-called power cone. This very general formulation unifies well-known problem classes such as linear and convex quadratic optimization, but also problem classes such as geometric programming or p-norm location problems. Moreover, we show that the power cone admits a self-concordant barrier with a low parameter, which implies that all problems belonging to the aforementioned class are solvable in polynomial time. Furthermore, recent nonsymmetric primal-dual interior-point methods can be used with that conic formulation. However, in order to formulate a given convex problem in a conic form with power cones, it is often necessary to add auxiliary variables, which increase computing time. In this work, we tackle this drawback with a new framework based on approximate partial minimization. Partial minimization removes the artificially introduced auxiliary variables in order to restore the efficiency of the algorithms. We show that polynomial complexity of standard interior-point methods can be preserved in this framework and demonstrate how it can be applied to concrete problem classes, along with numerical tests that display notable improvements both in terms of the computing time and of the number of iterations.(FSA 3) -- UCL, 200

An interior-point method for the single-facility location problem with mixed norms using a conic formulation

We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R, where each distance can be measured according to a different p-norm. We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved

Downloaded on June 21, 2014. The Journal of Clinical Investigation. More information at www.jci.org/articles/view/106516 Hypoxemia in Pulmonary Embolism, a Clinical Study

21 patients with no previous heart or lung disease shortly after an episode of acute pulmonary embolism. The diagnosis was based on pulmonary angiography demonstrating distinct vascular filling defects or "cutoffs. " It was found that virtually all of the hypoxemia in patients with previously normal heart and lungs could be accounted for on the basis of shunt-like effect. The magnitude of the shunting did not correlate with the percent of the pulmonary vascular bed occluded nor with the mean pulmonary artery pressure. The shunts tended to gradually recede over about a month after embolism. Patients without pulmonary infarction were able to inspire 80-111% of their predicted inspiratory capacities, and this maneuver temporarily diminished the observed shunt. Patients with pulmonary infarcts were able to inhale only to 60-69 % of predicted inspiratory capacity, and this did not reverse shunting. These data suggest that the cause of right-to-left shunting in patients with pulmonary emboli is predominantly atelectasis. When the elevation of mean pulmonary artery pressure was compared to cardiac index per unit of unoccluded lung, it fell within the range of pulmonary hypertension predicted from published data obtained in patients with exercise in all except one case. This observation suggests that pulmonary vasoconstriction following embolism is not important in humans, although these data are applicable only during the time interval in which our patients were studied and in patients receiving heparin