Several Schur complement-based preconditioners have been proposed for solving (generalized) saddlepoint problems. We consider probing-based methods for approximating those Schur complements in the preconditioners of the type proposed by [Murphy, Golub and Wathen ’00], [de Sturler and Liesen ’03] and [Siefert and de Sturler ’04]. This approach can be applied in similar preconditioners as well. W...

Spatial reserve design concerns the planning of biological reserves for conservation. Typical reserve selection formulations operate on a large set of landscape elements, which could be grid cells or irregular sites, and selection algorithms aim to select the set of sites that achieves biodiversity target levels with minimum cost. This study presents a completely different optimization approach...

Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programming relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints should be added to the relaxation. Typical...

Two methods for internally calibrating spectra resulting from the matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry analysis of partially digested proteins are described. Partial digestion of proteins results in a large number of ion signals present in the MALDI-TOF mass spectrum, which in turn represent a significant over-sampling of each amino acid prese...

We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~-2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the product AD2A v when A has dense columns; and (2) i...

We describe the analytic center cutting plane method and its relationship to classical methods of nondi erentiable optimization and column generation. Implementation issues are also discussed, and current applications listed. Keywords Projective Algorithm, Analytic Center, Cutting Plane Method. This work has been completed with support from the Fonds National Suisse de la Recherche Scienti que,...

The Kantorovich Theorem is a fundamental tool in nonlinear analysis which has been extensively used in classical numerical analysis. In this paper we show that it can also be used in analyzing interior point methods. We obtain optimal bounds for Newton’s method when relied upon in a path following algorithm for linear complementarity problems. Given a point z that approximates a point z(τ ) on ...

We consider computing the saddle points of a convex-concave function using subgradient methods. The existing literature on finding saddle points has mainly focused on establishing convergence properties of the generated iterates under some restrictive assumptions. In this paper, we propose a subgradient algorithm for generating approximate saddle points and provide per-iteration convergence rat...

The starting point used by an interior point algorithm for linear and convex quadratic programming may significantly influence the behaviour of the method. A widely used heuristic to construct such a point consists of dropping variable nonnegativity constraints and computing a solution which minimizes the Euclidean norm of the primal (or dual) point while satisfying the appropriate primal (or d...

The appearance of the Function Point technique has allowed the ICT community to increase significantly the practice of software measurement, with respect to the use of the traditional “Lines of Code approach”. A FP count, however, requires a complete and detailed level of descriptive documentation, like the Functional Specifications of the software system under measurement, to be performed. The...