scholarly journals Superlinear convergence of the control reduced interior point method for PDE constrained optimization

2007 ◽  
Vol 39 (3) ◽  
pp. 369-393 ◽  
Author(s):  
Anton Schiela ◽  
Martin Weiser
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Superlinear Convergence ◽  
Interior Point Method ◽  
Point Method ◽  
Pde Constrained Optimization

scholarly journals A weighted logarithmic barrier interior-point method for linearly constrained optimization

2021 ◽  
Vol 66 (4) ◽  
pp. 783-792
Author(s):  
Selma Lamri ◽  
◽  
Bachir Merikhi ◽  
Mohamed Achache ◽  
◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Point Method ◽  
Step Size ◽  
Positive Vector ◽  
Tangent Method ◽  
Linearly Constrained ◽  
Logarithmic Barrier

In this paper, a weighted logarithmic barrier interior-point method for solving the linearly convex constrained optimization problems is presented. Unlike the classical central-path, the barrier parameter associated with the per- turbed barrier problems, is not a scalar but is a weighted positive vector. This modi cation gives a theoretical exibility on its convergence and its numerical performance. In addition, this method is of a Newton descent direction and the computation of the step-size along this direction is based on a new e cient tech- nique called the tangent method. The practical e ciency of our approach is shown by giving some numerical results.

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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