刊名:Journal of Computational and Applied Mathematics
出版年:2017
出版时间:1 March 2017
年:2017
卷:312
期:Complete
页码:216-230
全文大小:465 K
文摘
In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716302254&_mathId=si1.gif&_user=111111111&_pii=S0377042716302254&_rdoc=1&_issn=03770427&md5=a9d860af925bdb94da8bbd95618e36a9" title="Click to view the MathML source">(SDP)pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> based on Alizadeh–Haeberly–Overton (ng class="boldFont">AHOng>) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem pan id="mmlsi2" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716302254&_mathId=si2.gif&_user=111111111&_pii=S0377042716302254&_rdoc=1&_issn=03770427&md5=63a215222196463013d69bc08131b583" title="Click to view the MathML source">(SDP)μpan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> and its convergence to optimal solution of pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716302254&_mathId=si1.gif&_user=111111111&_pii=S0377042716302254&_rdoc=1&_issn=03770427&md5=a9d860af925bdb94da8bbd95618e36a9" title="Click to view the MathML source">(SDP)pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan>. Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is pan id="mmlsi4" class="mathmlsrc">nce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716302254&_mathId=si4.gif&_user=111111111&_pii=S0377042716302254&_rdoc=1&_issn=03770427&md5=5eb89b208226c49f10c23fc9151a54eb">nlineImage" height="21" width="171" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716302254-si4.gif"><noscript>n:bottom" width="171" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0377042716302254-si4.gif">noscript>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan>. Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work.