An Interior Point Method for Linear Programming Using Weighted Analytic Centers

2009 ◽  
Vol 41 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Julianne Anderson ◽  
Shafiu Jibrin
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Analytic Centers

A new efficient short-step projective interior point method for linear programming

2018 ◽  
Vol 46 (3) ◽  
pp. 291-294
Author(s):  
Mousaab Bouafia ◽  
Djamel Benterki ◽  
Adnan Yassine
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method

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.

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