Quasi-Newton acceleration for equality-constrained minimization

Authors:
L. Ferreira-Mendonça;V. L. Lopes;J. M. Martínez
Affiliations:
Department of Computer Science, IM-UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil 21941-590;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970
Venue:
Computational Optimization and Applications
Year:
2008

Citing 20
Cited 1

A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds

SIAM Journal on Numerical Analysis
Convergence of quasi-Newton matrices generated by the symmetric rank one update

Mathematical Programming: Series A and B
Inexact Newton methods for solving nonsmooth equations

Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Local Convergence of the Symmetric Rank-One Iteration

Computational Optimization and Applications
Validation of an Augmented Lagrangian Algorithm with a Gauss-Newton Hessian Approximation Using a Set of Hard-Spheres Problems

Computational Optimization and Applications
Duality-based domain decomposition with natural coarse-space for variational inequalities0

Journal of Computational and Applied Mathematics
Practical quasi-Newton methods for solving nonlinear systems

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Algorithm 813: SPG—Software for Convex-Constrained Optimization

ACM Transactions on Mathematical Software (TOMS)
Nonmonotone Spectral Projected Gradient Methods on Convex Sets

SIAM Journal on Optimization
On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods

SIAM Journal on Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients

Computational Optimization and Applications
Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints

SIAM Journal on Optimization
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization

ACM Transactions on Mathematical Software (TOMS)
A primal-dual trust region algorithm for nonlinear optimization

Mathematical Programming: Series A and B
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

SIAM Review
Inexact Semimonotonic Augmented Lagrangians with Optimal Feasibility Convergence for Convex Bound and Equality Constrained Quadratic Programming

SIAM Journal on Numerical Analysis
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems

Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent

ACM Transactions on Mathematical Software (TOMS)
On Augmented Lagrangian Methods with General Lower-Level Constraints

SIAM Journal on Optimization

Improving ultimate convergence of an augmented Lagrangian method

Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday

Quantified Score

Hi-index	0.00

Visualization

Abstract

Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this paper quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms, with equality constraints. A periodically-restarted memoryless symmetric rank-one (SR1) correction method is introduced for that purpose. Convergence results are given and numerical experiments that confirm that the acceleration is effective are presented.