A working set SQCQP algorithm with simple nonmonotone penalty parameters

作者：Tang, Chun Ming; Jian, Jin Bao^*; Li, Guo Yin

来源：Journal of Computational and Applied Mathematics, 2011, 236(6): 1382-1398.

DOI：10.1016/j.cam.2011.09.002

• SQCQP
• Quadratically constrained quadratic programming
• Working set
• Nonmonotone penalty parameters
• Superlinear convergence

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.

• 出版日期2011-10-15
• 单位广西大学