We study the concept of quadratic variation a continuous path along sequence partitions and its dependence with respect to choice partition sequence. introduce roughness show that for Hölder-continuous paths satisfying this condition, balanced is invariant Typical Brownian motion are shown satisfy property almost-surely any required step size condition. Using these results we derive formulation...

We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler–Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms ...

The support function of a free-form–surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and its support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study offset surfaces and isophotes (which are simp...

We consider coordinate descent methods on convex quadratic problems, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic problems for which the random-permutations version of cyclic coordinate descent (RPCD) outperforms the standard cyclic ...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...

Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasible region. Binary classification is posed as a quadratically constrained quadrat...

Title of dissertation: Adaptive Constraint Reduction for Convex Quadratic Programming and Training Support Vector Machines Jin Hyuk Jung, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dianne P. O’Leary Department of Computer Science Convex quadratic programming (CQP) is an optimization problem of minimizing a convex quadratic objective function subject to linear constraints. We...