A method combining norm-relaxed QCQP subproblems with active set identification for inequality constrained optimization

ABSTRACT

In this paper, an adaptation of the sequential quadratically constrained quadratic programming method is proposed to solve inequality constrained minimization. At each iteration, it solves a norm-relaxed quadratically constrained quadratic programming subproblem that uses an active set identification technique to reduce the scale and computational cost. By taking a valid line search, the iterates always get into the feasible set after a finite number of iterations, and followed by a suitable update rule for the penalty parameters. Under suitable conditions without the strict complementarity, our method has the global and superlinear convergence properties. In addition, numerical results are reported to demonstrate the efficiency of the proposed method.

Keywords:

• Inequality constrained optimization
• SQCQP
• active set identification
• global convergence
• superlinear convergence

Mathematics Subject Classifications (2000):

• 90C30
• 49M37
• 65K05

Acknowledgements

The authors are grateful to the editors and anonymous referees for their valuable comments and suggestions to improve the earlier draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11771383 and 11761013], Natural Science Foundation of Guangxi Province [grant numbers 2018GXNSFFA281007 and 2018GXNSFAA281099], Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi Province [grant number 2017KY0540] and Innovative Project of Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing [grant number 2016CSOBDP002].