scholarly journals Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Jinbao Jian ◽  
Hanjun Zeng ◽  
Guodong Ma ◽  
Zhibin Zhu
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Nonlinear Constrained Optimization ◽  
Primal Dual

A Globally and Superlinearly Convergent Primal-dual Interior Point Method for General Constrained Optimization

2015 ◽  
Vol 8 (3) ◽  
pp. 313-335 ◽  
Author(s):  
Jianling Li ◽  
Jian Lv ◽  
Jinbao Jian
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Point Method ◽  
Active Set ◽  
Primal Dual ◽  
Systems Of Linear Equations ◽  
Working Set

AbstractIn this paper, a primal-dual interior point method is proposed for general constrained optimization, which incorporated a penalty function and a kind of new identification technique of the active set. At each iteration, the proposed algorithm only needs to solve two or three reduced systems of linear equations with the same coefficient matrix. The size of systems of linear equations can be decreased due to the introduction of the working set, which is an estimate of the active set. The penalty parameter is automatically updated and the uniformly positive definiteness condition on the Hessian approximation of the Lagrangian is relaxed. The proposed algorithm possesses global and superlinear convergence under some mild conditions. Finally, some preliminary numerical results are reported.

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