A novel strategy to optimize consensus classifiers for large classification problems is proposed, based on Linear Programming (LP) techniques and the recently introduced Maximum Feasibility (MaxF) heuristic for solving infeasible LP problems. For a set of classifiers and their normalized class dependent scores one postulates that the consensus score is a linear combination of individual scores....

A piece of code in a computer program is infeasible if it cannot be part of any normallyterminating execution of the program. We develop an algorithm for the automatic detection of all infeasible code in a program. We first translate the task of determining all infeasible code into the problem of finding all statements that can be covered by a feasible path. We prove that in order to identify a...

Interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [31], these off-central paths are shown to be well-defined analytic curves ...

The Jacobi–Davidson method is a popular technique to compute a few eigenpairs of large sparse matrices. Its introduction, about a decade ago, was motivated by the fact that standard eigensolvers often require an expensive factorization of the matrix to compute interior eigenvalues. Such a factorization may be infeasible for large matrices as arise in today’s large-scale simulations. In the Jaco...

A class of primal dual interior point methods is developed These methods use a higher order Taylor polynomial to approximate a primal dual trajectory de ned from an infeasible point A detailed implementation of these methods is given and their computational performance is studied We give computational results for two di erent approaches for de ning trajectory and using up to th order polynomial...

Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an affine set. It is described in detail how ...

We present a constraint analysis methodology for Linear Matrix Inequality (LMI) constraints. If the constraint set is found to be feasible we search for a minimal representation; otherwise, we search for an irreducible infeasible system. The work is based on the solution of a set covering problem where each row corresponds to a sample point and is determined by constraint satisfaction at the sa...

Several issues concerning an analysis of large and sparse linear programming problems prior to solving them with an interior point based optimizer are addressed in this paper. Three types of presolve procedures are distinguished. Routines from the rst class repeatedly analyze an LP problem formulation: eliminate empty or singleton rows and columns, look for primal and dual forcing or dominated ...

A modiication of the (infeasible) primal{dual interior point method is developed. The method uses multiple corrections to improve the centrality of the current iterate. The maximum number of corrections the algorithm is encouraged to make depends on the ratio of the eeorts to solve and to factorize the KKT systems. For any LP problem, this ratio is determined right after preprocessing the KKT s...