Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک ایرانیان IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 7 14 8888 13 en jalali 1396 1 1 gregorian 2017 4 1 12 1 online 1 fulltext
en An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function تخصصي Special پژوهشي Research paper <p></p> <p align="center" dir="RTL"></p> <p align="center" dir="RTL"></p> <p>In this paper, we&nbsp;consider convex quadratic semidefinite optimization problems and&nbsp;provide a primal-dual Interior Point Method (IPM) based on a new&nbsp;kernel function with a trigonometric barrier term. Iteration&nbsp;complexity of the algorithm is analyzed using some easy to check&nbsp;and mild conditions. Although our proposed kernel function is&nbsp;neither a Self-Regular (SR) function nor logarithmic barrier&nbsp;function, the primal-dual IPMs based on this kernel function enjoy&nbsp;the worst case iteration bound \$Oleft(sqrt{n}log nlog&nbsp;frac{n}{epsilon}right)\$ for the large-update methods with the&nbsp;special choice of its parameters. This bound coincides to the so&nbsp;far best known complexity results obtained from SR kernel&nbsp;functions for linear and semidefinite optimization problems.&nbsp;Finally some numerical issues regarding the practical performance&nbsp;of the new proposed kernel function is reported.</p> Convex quadratic semidefinite optimization problem, Primal-dual interior-point methods, Kernel function, Iteration complexity. 131 152 http://ijmsi.ir/browse.php?a_code=A-10-1111-1&slc_lang=en&sid=1 M. R. Peyghami peyghami@kntu.ac.ir `10031947532846003944` 10031947532846003944 Yes K.N. Toosi Univ. of Tech. S. Fathi Hafshejani sajadfathi85@gmail.com `10031947532846003945` 10031947532846003945 No Shiraz Univ. of Tech.