4,493 research outputs found
Multi-threading a state-of-the-art maximum clique algorithm
We present a threaded parallel adaptation of a state-of-the-art maximum clique
algorithm for dense, computationally challenging graphs. We show that near-linear speedups
are achievable in practice and that superlinear speedups are common. We include results for
several previously unsolved benchmark problems
Multipoint secant and interpolation methods with nonmonotone line search for solving systems of nonlinear equations
Multipoint secant and interpolation methods are effective tools for solving
systems of nonlinear equations. They use quasi-Newton updates for approximating
the Jacobian matrix. Owing to their ability to more completely utilize the
information about the Jacobian matrix gathered at the previous iterations,
these methods are especially efficient in the case of expensive functions. They
are known to be local and superlinearly convergent. We combine these methods
with the nonmonotone line search proposed by Li and Fukushima (2000), and study
global and superlinear convergence of this combination. Results of numerical
experiments are presented. They indicate that the multipoint secant and
interpolation methods tend to be more robust and efficient than Broyden's
method globalized in the same way
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
Computing Least Fixed Points of Probabilistic Systems of Polynomials
We study systems of equations of the form X1 = f1(X1, ..., Xn), ..., Xn =
fn(X1, ..., Xn), where each fi is a polynomial with nonnegative coefficients
that add up to 1. The least nonnegative solution, say mu, of such equation
systems is central to problems from various areas, like physics, biology,
computational linguistics and probabilistic program verification. We give a
simple and strongly polynomial algorithm to decide whether mu=(1, ..., 1)
holds. Furthermore, we present an algorithm that computes reliable sequences of
lower and upper bounds on mu, converging linearly to mu. Our algorithm has
these features despite using inexact arithmetic for efficiency. We report on
experiments that show the performance of our algorithms.Comment: Published in the Proceedings of the 27th International Symposium on
Theoretical Aspects of Computer Science (STACS). Technical Report is also
available via arxiv.or
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