A primal-dual interior-point algorithm for symmetric optimization based on a new kernel function with trigonometric barrier term yielding the best known iteration bounds

2016 ◽  
Vol 28 (3-4) ◽  
pp. 389-406 ◽  
Author(s):  
B. Kheirfam
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Algorithm ◽  
Symmetric Optimization ◽  
Primal Dual

scholarly journals An interior point algorithm for solving linear optimization problems using a new trigonometric kernel function

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1471-1486
Author(s):  
S. Fathi-Hafshejani ◽  
Reza Peyghami
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Worst Case ◽  
Complexity Bounds ◽  
Linear Optimization Problems ◽  
Primal Dual ◽  
The Given

In this paper, a primal-dual interior point algorithm for solving linear optimization problems based on a new kernel function with a trigonometric barrier term which is not only used for determining the search directions but also for measuring the distance between the given iterate and the ?-center for the algorithm is proposed. Using some simple analysis tools and prove that our algorithm based on the new proposed trigonometric kernel function meets O (?n log n log n/?) and O (?n log n/?) as the worst case complexity bounds for large and small-update methods. Finally, some numerical results of performing our algorithm are presented.

scholarly journals A Parametric Kernel Function Generating the best Known Iteration Bound for Large-Update Methods for CQSDO

2020 ◽  
Vol 8 (4) ◽  
pp. 876-889
Author(s):  
Guerra Loubna ◽  
Achache Mohamed
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Numerical Results ◽  
Interior Point Algorithm ◽  
Iteration Bound ◽  
Primal Dual

In this paper, we propose a large-update primal-dual interior point algorithm for convex quadratic semidefiniteoptimization (CQSDO) based on a new parametric kernel function. This kernel function is a parameterized version of the kernel function introduced by M.W. Zhang (Acta Mathematica Sinica. 28: 2313-2328, 2012) for CQSDO. The investigation according to it generating the best known iteration bound O for large-update methods. Thus improves the iteration bound obtained by Zhang for large-update methods. Finally, we present few numerical results to show the efficiency of the proposed algorithm.

scholarly journals A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

2020 ◽  
Vol 28 (1) ◽  
pp. 27-41
Author(s):  
Benhadid Ayache ◽  
Saoudi Khaled
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Linear Optimization ◽  
Kernel Functions ◽  
Special Choice ◽  
Interior Point Algorithm ◽  
Double Barrier ◽  
New Class ◽  
Iteration Bound ◽  
Primal Dual

AbstractIn this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O\sqrt n \log (n)\log \left( {{n \over \in }} \right) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm.

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