Primal-dual interior point QP-free algorithm for nonlinear constrained optimization
 作者： Jinbao Jian,  Hanjun Zeng,  Guodong Ma,  Zhibin Zhu 作者单位： 1Yulin Normal University2Guangxi University3Guilin University of Electronic Technology 刊名： Journal of Inequalities and Applications, 2017, Vol.2017 (1) 来源数据库： Springer Journal DOI： 10.1186/s13660-017-1500-2 关键词： Inequality and equality constraints;  Optimization;  Primal-dual interior method;  Working set;  Global and superlinear convergence;  90C30;  49M37;  65K05; 英文摘要： In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of linear equations with a common coefficient matrix, where a slightly new working set technique for judging the active set is used to construct the coefficient matrix, and the positive definiteness restriction on the Lagrangian Hessian estimate is relaxed. Under reasonable conditions, the proposed algorithm is globally and superlinearly convergent. During the numerical experiments, by modifying the technique in... Section 5 of (SIAM J. Optim. 14(1): 173-199, 2003 ), we introduce a slightly new computation measure for the Lagrangian Hessian estimate based on second order derivative information, which can satisfy the associated assumptions. Then, the proposed algorithm is tested and compared on 59 typical test problems, which shows that the proposed algorithm is promising. 原始语种摘要： In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of linear equations with a common coefficient matrix, where a slightly new working set technique for judging the active set is used to construct the coefficient matrix, and the positive definiteness restriction on the Lagrangian Hessian estimate is relaxed. Under reasonable conditions, the proposed algorithm is globally and superlinearly convergent. During the numerical experiments, by modifying the technique in... Section 5 of (SIAM J. Optim. 14(1): 173-199, 2003 ), we introduce a slightly new computation measure for the Lagrangian Hessian estimate based on second order derivative information, which can satisfy the associated assumptions. Then, the proposed algorithm is tested and compared on 59 typical test problems, which shows that the proposed algorithm is promising.

• algorithm　算法
• equality　相等
• estimate　估计
• constrained　约束
• point
• interior　内部的
• proposed　建议的
• optimization　最佳化
• working　开采
• nonlinear　非线性的