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:: Volume 12, Number 1 (4-2017) ::
Back to browse issues page IJMSI 2017, 12(1): 131-152
An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function
M. R. Peyghami , S. Fathi Hafshejani
Abstract:  

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) function nor logarithmic barrier function, the primal-dual IPMs based on this kernel function enjoy the worst case iteration bound $Oleft(sqrt{n}log nlog frac{n}{epsilon}right)$ for the large-update methods with the special choice of its parameters. This bound coincides to the so far best known complexity results obtained from SR kernel functions for linear and semidefinite optimization problems. Finally some numerical issues regarding the practical performance of the new proposed kernel function is reported.

Keywords: Convex quadratic semidefinite optimization problem, Primal-dual interior-point methods, Kernel function, Iteration complexity.
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Type of Study: Research | Subject: Special
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Peyghami M R, Fathi Hafshejani S. An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function. IJMSI. 2017; 12 (1) :131-152
URL: http://ijmsi.ir/article-1-671-en.html
Back to browse issues page Volume 12, Number 1 (4-2017)
نشریه علوم ریاضی و انفورماتیک Iranian Journal of Mathematical Sciences and Informatics
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