A simply sequential quadratically constrained quadratic programming method of strongly sub-feasible directions for constrained optimization

Abstract

This article presents a simply sequential quadratically constrained quadratic programming method of strongly sub-feasible directions for constrained optimization. The main direction is obtained by solving one subproblem which consists of a convex quadratic objective function, simply convex quadratic constraints. In order to avoid Maratos effect, correct the main search direction by a system of linear equations. In this work, we also present a new second-order approximate condition which is used to ensure that the unit step can be accepted. The global and superlinear convergence can be induced under some suitable conditions. In the end, we present a set of preliminary numerical experiments to illustrate the effectiveness of the method.

Keywords:

• sequential quadratically constrained quadratic programming
• systems of linear equations
• strongly sub-feasible directions
• second-order approximate condition
• global convergence
• rate of convergence

AMS Subject Classifications::

• 90C30
• 49M37
• 65K05

Acknowledgements

This project was supported by NSFC (No. 10771040) and Guangxi Science Foundation (Nos. 2011GXNSFD018022, 0832025) of China.