integrals
particular class
85-103
path parameters
tangent
curvature integral
false
solution
first-order methods
integrand
feasible solution
point
In this paper we study a particular class of primal-dual path-following methods which try to follow a trajectory of interior feasible solutions in primal-dual space toward an optimal solution to the primal and dual problem. The methods investigated are so-called first-order methods: each iteration consists of a “long” step along the tangent of the trajectory, followed by explicit recentering steps to get close to the trajectory again. It is shown that the complexity of these methods, which can be measured by the number of points close to the trajectory which have to be computed in order to achieve a desired gain in accuracy, is bounded by an integral along the trajectory. The integrand is a suitably weighted measure of the second derivative of the trajectory with respect to a distinguished path parameter, so the integral may be loosely called a curvature integral.
complexity
articles
https://doi.org/10.1007/bf01182599
program
interior feasible solution
second derivative
Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals
iteration
primal-dual space
measures
number of points
method
path-following method
1993-01
space
dual problem
respect
2022-08-04T16:50
gain
parameters
paper
order
article
1993-01-01
weighted measure
linear program
step
number
accuracy
trajectories
problem
primal-dual path-following method
optimal solution
https://scigraph.springernature.com/explorer/license/
derivatives
class
Zhao
G.
Springer Nature
1432-0606
Applied Mathematics & Optimization
0095-4616
10.1007/bf01182599
doi
1
Stoer
J.
Numerical and Computational Mathematics
Mathematical Sciences
Springer Nature - SN SciGraph project
27
dimensions_id
pub.1053613854
Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, W-8700, Würzburg, Germany
Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, W-8700, Würzburg, Germany