scholarly journals A weighted full-Newton step primal-dual interior point algorithm for convex quadratic optimization

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Achache Mohamed
Keyword(s):  
Interior Point ◽  
Quadratic Optimization ◽  
Interior Point Algorithm ◽  
Convex Quadratic Optimization ◽  
Newton Step ◽  
Primal Dual ◽  
Full Newton Step

A polynomial-time weighted path-following interior-point algorithm for linear optimization

2018 ◽  
Vol 13 (02) ◽  
pp. 2050038
Author(s):  
Mohamed Achache
Keyword(s):  
Polynomial Time ◽  
Interior Point ◽  
Line Search ◽  
Linear Optimization ◽  
Path Following ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Iteration Bound ◽  
Primal Dual ◽  
Full Newton Step

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an [Formula: see text]-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, [Formula: see text]. This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.

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