http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:12843 Piecewise affine functions arise from Lagrangian duals of integer programming problems, and optimizing them provides good bounds for use in a branch and bound method. Methods such as the subgradient method and bundle methods assume only one subgradient is available at each point, but in many situations there is more information available. We present a new method for optimizing such functions, which is related to steepest descent, but uses an outer approximation to the subdifferential to avoid some of the numerical problems with the steepest descent approach. We provide convergence results for a class of outer approximations, and then develop a practical algorithm using such an approximation for the compact dual to the linear programming relaxation of the uncapacitated facility location problem. We make a numerical comparison of our outer approximation method with the projection method of Conn and Cornuéjols, and the bundle method of Schramm and Zowe. 2013-05-02T01:46:25.205Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:5981 Facility Location can be seen as a whole family of problems which have many obvious applications in economics. They have been widely explored in the Operations Research community, from the viewpoints of approximation, heuristics, linear programming, etc. We add a new facet by initiating the study of some of these problems from a parametric point of view. Moreover, we exhibit some less obvious applications of these algorithms in the processing of semistructured documents and in computational biology. 2010-04-27T04:42:14.625Z ]]>