For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to a max-min problem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over ...

The main issue of this work is to investigate asymmetric structures in graphs. While symmetry structures in graphs are well observed, the opposite question has not been investigated deeply so far. It is known from a theorem of Wright, that almost all graphs are asymmetric. The class of asymmetric graphs is restricted further by forbidding even local symmetries. The main question is to determine...

A nonempty closed convex polyhedron X can be represented either as X = {x: Ax < b}, where (A, b) are given, in which case X is called an H-cell, or in the form X= {x: x = UA + V , A1, A 0, z 0}, where (U, V) are given, in which case X is called a W-cell. This note discusses the computational complexity of certain set containment problems. The problems of determining if X e Y, where (i) X is an ...

In performing regularized set. operations on two solids, the most difficult step is boundary classification, in which the boundaries of each solid are split into portions that are inside, outside, or on the surface of the other solid. In this paper, we present a method for doing boundary classification on polyhedral solids and give measurements of the algorithm's time complexity on a number of ...

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established...

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...

The paper describes a method for generating combinatorial complexes of polyhedral type. Building blocks B are implanted into the maximal simplices of a simplicial complex C, on which a group operates as a combinatorial reflection group. Of particular interest is the case where B is a polyhedral block and C the barycentric subdivision of a regular incidence-polytope K together with the action of...

Let I = (Z, 26, 6, B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of Q(I) whose maximal cells are the quadrangles of Q(I) shared by a voxel of B in the foreground – the object under study – and by a voxel of Z rB in the background – the ambient space. We show how to simplify the combinatorial structure of ∂Q(I) and obtain a 3D polyhedral com...