scholarly journals A numerical feasible interior point method for linear semidefinite programs

2007 ◽  
Vol 41 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Djamel Benterki ◽  
Jean-Pierre Crouzeix ◽  
Bachir Merikhi
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Semidefinite Programs

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

scholarly journals A parallel primal–dual interior-point method for semidefinite programs using positive definite matrix completion

2006 ◽  
Vol 32 (1) ◽  
pp. 24-43 ◽  
Author(s):  
Kazuhide Nakata ◽  
Makoto Yamashita ◽  
Katsuki Fujisawa ◽  
Masakazu Kojima
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Matrix Completion ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Point Method ◽  
Semidefinite Programs ◽  
Primal Dual

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

scholarly journals A tailored inexact interior-point method for systems analysis

2008 ◽  
Author(s):  
Janne Harju Johansson ◽  
Anders Hansson
Keyword(s):  
Interior Point ◽  
Systems Analysis ◽  
Interior Point Method ◽  
Point Method
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