A working set SQCQP algorithm with simple nonmonotone penalty parameters

Authors:
Chun-Ming Tang;Jin-Bao Jian;Guo-Yin Li
Affiliations:
College of Mathematics and Information Science, Guangxi University, Nanning 530004, PR China;College of Mathematics and Information Science, Guangxi University, Nanning 530004, PR China;Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 11
Cited 0

An outer-approximation algorithm for a class of mixed-integer nonlinear programs

Mathematical Programming: Series A and B
Exact penalty function algorithm with simple updating of the penalty parameter

Journal of Optimization Theory and Applications
CUTE: constrained and unconstrained testing environment

ACM Transactions on Mathematical Software (TOMS)
Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems

Journal of Optimization Theory and Applications
A Superlinearly Convergent Sequential Quadratically Constrained Quadratic Programming Algorithm for Degenerate Nonlinear Programming

SIAM Journal on Optimization
On the Accurate Identification of Active Constraints

SIAM Journal on Optimization
A Sequential Quadratically Constrained Quadratic Programming Method for Differentiable Convex Minimization

SIAM Journal on Optimization
On the Sequential Quadratically Constrained Quadratic Programming Methods

Mathematics of Operations Research
A Smoothing Newton-Type Algorithm of Stronger Convergence for the Quadratically Constrained Convex Quadratic Programming

Computational Optimization and Applications
On local convergence of sequential quadratically-constrained quadratic-programming type methods, with an extension to variational problems

Computational Optimization and Applications
A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms.