We construct a relative Chow-Künneth decomposition for a conic bundle over a surface such that the middle projector gives the Prym variety of the associated double covering of the discriminant of the conic bundle. This gives a refinement (up to an isogeny) of Beauville’s theorem on the relation between the intermediate Jacobian of the conic bundle and the Prym variety of the double covering.

We establish polynomial-time convergence of infeasible-interior-point methods for conic programs over symmetric cones using a wide neighborhood of the central path. The convergence is shown for a commutative family of search directions used in Schmieta and Alizadeh [9]. These conic programs include linear and semidefinite programs. This extends the work of Rangarajan and Todd [8], which establi...

Abstract This paper describes the conic operator splitting method (COSMO) solver, an algorithm and associated software package for convex optimisation problems with quadratic objective function constraints. At each step, alternates between solving a quasi-definite linear system constant coefficient matrix projection onto sets. The low per-iteration computational cost makes particularly efficien...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

Conic section is one of the geometric elements most commonly used for shape expression and mechanical accessory cartography. A rational quadratic Bézier curve is just a conic section. It cannot represent an elliptic segment whose center angle is not less than . However, conics represented in rational quartic format when compared to rational quadratic format, enjoy better properties such as bein...

H. J. Kong Jin Choi J. S. Shin S. W. Yi B. G. Jeon Korea Advanced Institute of Science and Technology Department of Physics Daejeon 305-701, Korea E-mail: [email protected] Abstract. By numerical simulations, it has been shown that a conventional cylindrical rod can be used as a hollow conic beam generator by illuminating a parallel laser beam inclined to the axis of the rod. Half of the conic...

We consider the problem of computing a restricted nonnegative matrix factorization (NMF) of an m × n matrix X . Specifically, we seek a factorization X ≈ BC, where the k columns of B are a subset of those from X and C ∈ Rk×n ≥0 . Equivalently, given the matrix X , consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S ε-approximates the conic hull o...

Catadioptric systems consist of the combination of lenses and mirrors. From them, central panoramic systems stand out because they provide a unique effective viewpoint, leading to the well-known unifying theory for central catadioptric systems. This paper considers catadioptric systems consisting of a conic mirror and a projective camera. Although a system with conic mirror does not possess a s...

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as a function of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity an...