Interior point solvers for semidefinite programming (SDP) have evolved a great deal in the last decade, and their development continues. In order to further support and encourage this development, we present a new test set of SDP instances. These instances arise from recent applications of SDP in coding theory, computational geometry, graph theory and truss topology design. Most of these instan...

Abstract In many fields of computer science such as computer animation, computer graphics, computer aided geometric design and robotics, it is a common problem to detect the positional relationships of several entities. Based on generalized characteristic polynomials and projective transformations, we derive algebraic conditions for detecting the various positional relationships of two planar c...

In this paper, we formulate the blind equalization of Constant Modulus (CM) signals as a convex optimization problem. This is done by performing an algebraic transformation on the direct formulation of the equalization problem and then restricting the set of design variables to a subset of the original feasible set. In particular, we express the blind equalization problem as a linear objective ...

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers gene...

Let M be the interior of a compact, orientable 3–manifold with non-empty boundary a disjoint union of tori, and T be an ideal triangulation of M . The affine algebraic set D(M ; T ), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T , is defined and compactified by adding projective classes of transversely measured singular codimension–one foliations of (M...

We present a quadtree-based decomposition of the interior of a polygon with holes. The complete decomposition yields a constant factor approximation of the minimum weight Steiner triangulation (MWST) of the polygon. We show that this approximate MWST supports ray shooting queries in the query-sensitive sense as deened by Mitchell, Mount and Suri. A proper truncation of our quadtree-based decomp...

This paper focuses on completeness results about generic expansions of propositional Weak Nilpotent Minimum (WNM) logics with truth-constants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) the t-norm is a Weak Nilpotent Minimum ...

In this paper we develop a Real Time Optimization (RTO) strategy for a silicon reactor. The reactor dynamics are described using parabolic partial differential equations with countercurrent liquid, gas and solid flow with chemical reaction. The model equations are converted to a system of differential algebraic equations using the method of lines and up-winding approximation for the spatial der...

In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and p respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the necessity of b ≤ 2 i+7. We sketch three proofs of this fact: the original one by Scott [Sco76], an elementary one, and one using algebraic geometry. As a refinem...