Acceleration and Parallelization of the Path-Following Interior Point Method for a Linearly Constrained Convex Quadratic Problem

1991 ◽  
Vol 1 (4) ◽  
pp. 548-564 ◽  
Author(s):  
Y. Nesterov ◽  
A. Nemirovsky
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Path Following ◽  
Point Method ◽  
Quadratic Problem ◽  
Linearly Constrained

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 first-order interior-point method for linearly constrained smooth optimization

2009 ◽  
Vol 127 (2) ◽  
pp. 399-424 ◽  
Author(s):  
Paul Tseng ◽  
Immanuel M. Bomze ◽  
Werner Schachinger
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
First Order ◽  
Linearly Constrained ◽  
Smooth Optimization

New complexity analysis of a full Nesterov–Todd step interior-point method for semidefinite optimization

2017 ◽  
Vol 10 (04) ◽  
pp. 1750070 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Path Following ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Line Searches ◽  
Complexity Result ◽  
Primal Dual

In this paper, we propose a new primal-dual path-following interior-point method for semidefinite optimization based on a new reformulation of the nonlinear equation of the system which defines the central path. The proposed algorithm takes only full Nesterov and Todd steps and therefore no line-searches are needed for generating the new iterations. The convergence of the algorithm is established and the complexity result coincides with the best-known iteration bound for semidefinite optimization problems.

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