In this work we present a quantum algorithm for multiobjective combinatorial optimization. We show that the adiabatic algorithm of Farhi et al. [arXiv:quant-ph/0001106] can be used by mapping a multiobjective combinatorial optimization problem onto a Hamiltonian using a convex combination among objectives. We present mathematical properties of the eigenspectrum of the associated Hamiltonian and...

The probability of error of classification methods based on convex combinations of simple base classifiers by “boosting” algorithms is investigated. We show in this talk that certain regularized boosting algorithms provide Bayes-risk consistent classifiers under the only assumption that the Bayes classifier may be approximated by a convex combination of the base classifiers. Non-asymptotic dist...

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, the adjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordina...

Local versions of the Minkowski tensors of convex bodies in ndimensional Euclidean space are introduced. An extension of Hadwiger’s characterization theorem for the intrinsic volumes, due to Alesker, states that the continuous, isometry covariant valuations on the space of convex bodies with values in the vector space of symmetric p-tensors are linear combinations of modified Minkowski tensors....

We describe a method based on convex combinations for morphing corresponding pairs of tilings in IR. It is shown that the method always yields a valid morph when the boundary polygons are identical, unlike the standard linear morph.

This year at TREC 2003 we participated in the robust track and investigated the use of very simple retrieval rules based on convex combinations of similarity measures based on first and second order features.

We first characterize ρ-monotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents. 2000 Mathematics Subject Classification: 32F45, 34G20, 46G20, 46T25, 47H05, 47H09, 47H10, 47H20.

Contents 1 The basic concepts 1 1.1 Is convexity useful? 1 1.2 Nonnegative vectors 4 1.3 Linear programming 5 1.4 Convex sets, cones and polyhedra 6 1.5 Linear algebra and affine sets 11 1.6 Exercises 14 2 Convex hulls and Carathéodory's theorem 17 2.1 Convex and nonnegative combinations 17 2.2 The convex hull 19 2.3 Affine independence and dimension 22 2.4 Convex sets and topology 24 2.5 Carat...