scholarly journals A predictor-corrector path-following algorithm for symmetric optimization based on Darvay's technique

2014 ◽  
Vol 24 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Path Following ◽  
Euclidean Jordan Algebra ◽  
Symmetric Cone ◽  
Interior Point Algorithm ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Symmetric Cone Optimization ◽  
Predictor Corrector ◽  
Corrector Step ◽  
Predictor Step

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is o(?rlogr?/?), where r is the rank of Euclidean Jordan algebra.

A corrector–predictor path-following algorithm for semidefinite optimization

2014 ◽  
Vol 07 (02) ◽  
pp. 1450028 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Line Search ◽  
Optimization Problems ◽  
Path Following ◽  
Central Path ◽  
Semidefinite Optimization ◽  
Iteration Complexity ◽  
Proximity Measure ◽  
Corrector Step ◽  
Predictor Step ◽  
Path Following Algorithm

A corrector–predictor algorithm is proposed for solving semidefinite optimization problems. In each two steps, the algorithm uses the Nesterov–Todd directions. The algorithm produces a sequence of iterates in a neighborhood of the central path based on a new proximity measure. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has [Formula: see text] iteration complexity.

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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