An active set quasi-Newton method with projected search for bound constrained minimization

Authors:
Li Sun;Guoping He;Yongli Wang;Liang Fang
Affiliations:
Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, PR China;College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, PR China;College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, PR China;Department of Mathematics and System Science, Taishan University, Tai'an 271021, PR China and Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 15
Cited 0

Global convergence of a class of trust region algorithms for optimization with simple bounds

SIAM Journal on Numerical Analysis
On the limited memory BFGS method for large scale optimization

Mathematical Programming: Series A and B
Representations of quasi-Newton matrices and their use in limited memory methods

Mathematical Programming: Series A and B
Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems

Journal of Optimization Theory and Applications
A limited memory algorithm for bound constrained optimization

SIAM Journal on Scientific Computing
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)

Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
A Truncated Newton Algorithm for Large Scale Box Constrained Optimization

SIAM Journal on Optimization
Newton Methods For Large-Scale Linear Inequality-Constrained Minimization

SIAM Journal on Optimization
On the Accurate Identification of Active Constraints

SIAM Journal on Optimization
An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints

SIAM Journal on Optimization
Newton's Method for Large Bound-Constrained Optimization Problems

SIAM Journal on Optimization
Convergence of a Generalized SMO Algorithm for SVM Classifier Design

Machine Learning
A Truncated Newton Method for the Solution of Large-Scale Inequality Constrained Minimization Problems

Computational Optimization and Applications
Working Set Selection Using Second Order Information for Training Support Vector Machines

The Journal of Machine Learning Research
A New Active Set Algorithm for Box Constrained Optimization

SIAM Journal on Optimization

Quantified Score

Hi-index	0.09

Visualization

Abstract

We analyze an active set quasi-Newton method for large scale bound constrained problems. Our approach combines the accurate active set identification function and the projected search. Both of these strategies permit fast change in the working set. The limited memory method is employed to update the inactive variables, while the active variables are updated by simple rules. A further division of the active set enables the global convergence of the new algorithm. Numerical tests demonstrate the efficiency and performance of the present strategy and its comparison with some existing active set strategies.