A New Primal-Dual Interior-Point Algorithm for Convex Quadratic Symmetric Cone Optimization Based on a Parametric Kernel Function

2012 ◽  
Author(s):  
Guoqiang Wang ◽  
Fayan Wang
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Symmetric Cone ◽  
Interior Point Algorithm ◽  
Primal Dual ◽  
Symmetric Cone Optimization

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 primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization

2021 ◽  
Author(s):  
Joachim Dahl ◽  
Erling D. Andersen
Keyword(s):  
Interior Point ◽  
Significant Contribution ◽  
Symmetric Cone ◽  
Conic Optimization ◽  
Interior Point Algorithm ◽  
Quadratic Cone ◽  
3 Dimensional ◽  
Primal Dual ◽  
Practical Algorithm ◽  
Numerical Performance

AbstractA new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It is a generalization of the famous algorithm suggested by Nesterov and Todd for the symmetric conic case, and uses primal-dual scalings for nonsymmetric cones proposed by Tunçel. We specialize Tunçel’s primal-dual scalings for the important case of 3 dimensional exponential-cones, resulting in a practical algorithm with good numerical performance, on level with standard symmetric cone (e.g., quadratic cone) algorithms. A significant contribution of the paper is a novel higher-order search direction, similar in spirit to a Mehrotra corrector for symmetric cone algorithms. To a large extent, the efficiency of our proposed algorithm can be attributed to this new corrector.

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