20 research outputs found
A Quantum Interior Point Method for LPs and SDPs
We present a quantum interior point method with worst case running time
for
SDPs and for LPs, where the output of our algorithm is a pair of matrices
that are -optimal -approximate SDP solutions. The factor
is at most for SDPs and for LP's, and is
an upper bound on the condition number of the intermediate solution matrices.
For the case where the intermediate matrices for the interior point method are
well conditioned, our method provides a polynomial speedup over the best known
classical SDP solvers and interior point based LP solvers, which have a worst
case running time of and respectively. Our results
build upon recently developed techniques for quantum linear algebra and pave
the way for the development of quantum algorithms for a variety of applications
in optimization and machine learning.Comment: 32 page
Enumerating a subset of the integer points inside a Minkowski sum
AbstractSparse elimination exploits the structure of algebraic equations in order to obtain tighter bounds on the number of roots and better complexity in numerically approximating them. The model of sparsity is of combinatorial nature, thus leading to certain problems in general-dimensional convex geometry. This work addresses one such problem, namely the computation of a certain subset of integer points in the interior of integer convex polytopes. These polytopes are Minkowski sums, but avoiding their explicit construction is precisely one of the main features of the algorithm. Complexity bounds for our algorithm are derived under certain hypotheses, in terms of output-size and the sparsity parameters. A public domain implementation is described and its performance studied. Linear optimization lies at the inner loop of the algorithm, hence we analyze the structure of the linear programs and compare different implementations
A (3/2+ɛ) approximation algorithm for scheduling malleable and non-malleable parallel tasks
In this paper we study a scheduling problem with malleable and non-malleable parallel tasks on processors. A non-malleable parallel task is one that runs in parallel on a specific given number of processors. The goal is to find a non-preemptive schedule on the processors which minimizes the makespan, or the latest task completion time. The previous best result is the list scheduling algorithm with an absolute approximation ratio of . On the other hand, there does not exist an approximation algorithm for scheduling non-malleable parallel tasks with ratio smaller than , unless . In this paper we show that a schedule with length can be computed for the scheduling problem in time . Furthermore we present an approximation algorithm for scheduling malleable parallel tasks. Finally, we show how to extend our algorithms to the variant with additional release dates
Aplicación del método barrera logarítmica paramétrica a un programa convexo
En este trabajo, se describe una implementación natural del clásico Método de la
Función Barrera Logarítmica para un Programa Convexo Diferenciable. Para esto se
asume que las funciones objetivo y las funciones restricción satisfacen la condición de
lipschitz con constante de Lipschitz M > 0.
En el método propuesto, la búsqueda lineal se hace a lo largo de las direcciones
newton con respecto a la función barrera logarítmica estrictamente convexa cuando
estamos demasiado lejos de la trayectoria central, y cuando estamos demasiado
cerca de la trayectoria central con respecto a una métrica utilizada, solo reducimos el
parámetro de barrera.Trabado de investigacio