A Globally Convergent Filter Method for Nonlinear Programming

Authors:
Clóvis C. Gonzaga;Elizabeth Karas;Márcia Vanti
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2003

Citing 0
Cited 7

FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems

ACM Transactions on Mathematical Software (TOMS)
A filter-trust-region method for simple-bound constrained optimization

Optimization Methods & Software
A filter algorithm: comparison with NLP solvers

International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Two derivative-free algorithms for nonlinear equations

Optimization Methods & Software
Global convergence of a tri-dimensional filter SQP algorithm based on the line search method

Applied Numerical Mathematics
Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems

Computational Optimization and Applications
A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a feasibility phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally independent, and the only coupling between them is provided by the filter. The method is independent of the internal algorithms used in each iteration, as long as these algorithms satisfy reasonable assumptions on their efficiency. Under standard hypotheses, we show two results: for a filter with minimum size, the algorithm generates a stationary accumulation point; for a slightly larger filter, all accumulation points are stationary.