Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
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
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<p>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.</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
10031947532846006281
10031947532846006281
Yes
K.N. Toosi Univ. of Tech.
S.
Fathi Hafshejani
sajadfathi85@gmail.com
10031947532846006282
10031947532846006282
No
Shiraz Univ. of Tech.