关键词: 非线性规划, 序列二次规划, 信赖域, 相容性, 多维滤子

Abstract: Sequential quadratic programming(SQP)is one of the most effective methods for solving nonlinear programming(NLP)problems. However, due to the combination of trust region and SQP, there may be no solution(i.e. incompatibility). In view of incompatibility, a multidimensional compatible filter algorithm based on SQP and trust region is proposed. Firstly, according to the methods mentioned in the general literature, this paper introduces parameter variables to its constraints and punishes its objective function, which implements the feasibility treatment to overcome the incompatibility(i.e. without feasibility recovery stage). Secondly, this paper proposes a multi-dimensional filter condition to selectively accept the iteration step, thus avoiding the strict conditions of the traditional two-dimensional filter algorithm, which greatly relaxes the acceptance of the iteration step. Finally, we propose a modified multi-dimensional filter algorithm based on second-order correction strategy for possible effects. At the same time, the algorithm has global convergence under certain assumptions.

Key words: nonlinear programming, sequential quadratic programming, trust region, compatibility, multidimensional filtering