This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be … Read more
We examine the local convergence of a sequential semidefinite programming approach for solving nonlinear programs with nonlinear semidefiniteness constraints. Known convergence results are extended to slightly weaker second order sufficient conditions and the resulting subproblems are shown to have local convexity properties that imply a weak form of self-concordance of the barrier subproblems. CitationPreprint, Mathematisches … Read more
A support vector machine (SVM) determines whether a given observed pattern lies in a particular class. The decision is based on prior training of the SVM on a set of patterns with known classification, and training is achieved by solving a convex quadratic programming problem. Since there are typically a large number of training patterns, … Read more
We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to … Read more
We study a system of linear inequalities associated with the uncapacitated facility location problem. We show that this system defines a polytope with integer extreme points if and only if the graph does not contain a certain type of odd cycles. We also derive odd cycle inequalities and give a separation algorithm. ArticleDownload View PDF
It is shown that a compact storage implementation of a quasi-Newton method based on the adjoint Broyden update reduces in the affine case exactly to the well established GMRES procedure. Generally, storage and linear algebra effort per step are small multiples of n k, where n is the number of variables and k the number … Read more
We present a method to tune software parameters using ideas from software testing and machine learning. The method is based on the key observation that for many classes of instances, the software shows improved performance if a few critical parameters have “good” values, although which parameters are critical depends on the class of instances. Our … Read more
This paper describes a new primal relaxation for nonlinear integer programming problems with linear constraints. This relaxation, contrary to the standard Lagrangean relaxation, can be solved efficiently. It requires the solution of a nonlinear penalized problem whose linear constraint set is known only implicitly, but whose solution is made possible by the use of a … Read more
abstract CitationIn Proceeding of the International Conference: Mathematical Methods in Economics, Virt 2004, pp. 101-108, ISBN 80-8078-012-9ArticleDownload View PDF
We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and second-order necessary optimality conditions. We compare these relaxations with a basic semidefinite relaxation due to Shor, particularly in the context of branch-and-bound to determine a global optimal solution, where it is shown empirically that the new relaxations are significantly stronger. We … Read more