A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

作者：Jian, Jin bao^*; Ke, Xiao yan; Cheng, Wei xin

来源：Applied Mathematics and Computation, 2009, 214(2): 632-644.

DOI：10.1016/j.amc.2009.04.022

• Constrained optimization
• Norm-relaxed method
• Method of strongly sub-feasible directions
• SQP method
• Global convergence
• Superlinear convergence

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.

• 出版日期2009-8-15
• 单位河南师范大学; 广西大学