In this paper, we establish robustness to noise perturbations of polyhedral regularization of linear inverse problems. We provide a sufficient condition that ensures that the polyhedral face associated to the true vector is equal to that of the recovered one. This criterion also implies that the l2 recovery error is proportional to the noise level for a range of parameter. Our criterion is expr...

In this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second-order stochastic dominance constraints. By using the polyhedral properties of this dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We...

Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classifiers [7], is extended to the following: (i) Containment of one polyhedral set in another. (ii) Containment of a polyhedral set in a reverse-convex set defined by convex quadratic constraints. (iii) Containment of a general closed convex set, def...

This article studies the polyhedral structure of the 4-node network design problem (NDP). Using a theorem from the previous work of this author, the facets of the 4-node NDP can be translated into facets of larger size problems. The knowledge of complete polyhedral description of the 4-node NDP is important because it implies complete knowledge of 4-partition-based facets of larger NDPs. After ...

The polyhedral model for loop parallelization has proved to be an effective tool for advanced optimization and automatic parallelization of programs in higher-level languages. Yet, to integrate such optimizations seamlessly into production compilers, they must be performed on the compiler’s internal, low-level, intermediate representation (IR). With Polly, we present an infrastructure for polyh...

The polyhedral model is a powerful algebraic framework that has enabled significant advances to analyses and transformations of sequential affine (sub)programs, relative to traditional AST-based approaches. However, given the rapid growth of parallel software, there is a need for increased experiences with using polyhedral frameworks for analysis and transformations of explicitly parallel progr...

We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in Rn with Dirichlet boundary conditions. The weight is the distance to the set of singular boundary points. We give a detailed sketch of the proof in three dimensions.

This report describes an algoriUun thal computes the configuration space of a polyhedron willi planar motion relative La a fixed polyhedral obstacle. The algorilJlm decomposes the configuration space along Ule orienlation axis into intervals of cross-sections with the same structure. It computes the angles where the srrucrurc changes. In each interval between two changes, it computes the (fi:'\...

A k-nacci sequence in a finite group is a sequence of group elements x0, x1, x2, . . . , xn, . . . for which, given an initial seed set x0, x1, x2, . . . , xj−1 , each element is defined by xn x0x1 . . . xn−1, for j ≤ n < k, and xn xn−kxn−k 1 . . . xn−1, for n ≥ k. We also require that the initial elements of the sequence, x0, x1, x2, . . . , xj−1, generate the group, thus forcing the k-nacci s...