A globally convergent regularized interior point method for constrained optimization

2021 ◽  
pp. 1-36
Author(s):  
Songqiang Qiu
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Globally Convergent

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.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

scholarly journals An interior point method for isogeometric contact

2014 ◽  
Vol 276 ◽  
pp. 589-611 ◽  
Author(s):  
İ. Temizer ◽  
M.M. Abdalla ◽  
Z. Gürdal
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method
Sign in / Sign up

Export Citation Format

Share Document