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<dc:title xml:lang="pl"><![CDATA[A primal-dual interior point method for complex-variable optimization problems]]></dc:title>
<dc:creator><![CDATA[Laouar, Mounia]]></dc:creator>
<dc:creator><![CDATA[Brahimi, Mahmoud]]></dc:creator>
<dc:creator><![CDATA[Ziadi, Raouf]]></dc:creator>
<dc:creator><![CDATA[Saleh, Mohammed A.]]></dc:creator>
<dc:creator><![CDATA[Almaymuni, Abdulgader Z.]]></dc:creator>
<dc:creator><![CDATA[Alhalangy, Abdalilah]]></dc:creator>
<dc:subject xml:lang="pl"><![CDATA[convex optimization]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[complex variables]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[optimization problems]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[complex-valued kernel function]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[Newton direction]]></dc:subject>
<dc:description xml:lang="pl"><![CDATA[In this paper, we propose a primal-dual interior-point method for solving convex optimization problems with complex variables, relying on a newly defined complex-valued kernel function. We extend classical kernel functions to the complex domain by establishing appropriate differentiability and convexity properties that guarantee the well-posedness and convergence of the proposed algorithm.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[Our theoretical approach encompasses the formulation of penalized optimality conditions, the definition of a modified Newton direction tailored to complex parametrization, and the design of a central pathtracking algorithm featuring adaptive barrier parameter updating. A rigorous complexity analysis yields polynomial bounds depending on the problem dimension and the desired accuracy. Numerical experiments on large-scale complex-variable problems demonstrate both the effectiveness and robustness of the proposed approach.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[The results validate the algorithm?s dimension-independence property, with iteration counts remaining stable across substantial increases in problem size, and reveal significant computational advantages over state-of-the-art general-purpose solvers including IPOPT (Interior Point Optimizer). This work advances the theoretical foundations of interior-point methods in the complex domain and opens new perspectives for high-dimensional complex optimization.]]></dc:description>
<dc:publisher><![CDATA[Zielona Góra: Uniwersytet Zielonogórski]]></dc:publisher>
<dc:contributor><![CDATA[Korbicz, Józef (1951- ) - red.]]></dc:contributor>
<dc:contributor><![CDATA[Uciński, Dariusz - red.]]></dc:contributor>
<dc:date><![CDATA[2026]]></dc:date>
<dc:type xml:lang="pl"><![CDATA[artykuł]]></dc:type>
<dc:identifier><![CDATA[http://zbc.uz.zgora.pl/Content/96416/amcs-2026-0013.pdf]]></dc:identifier>
<dc:identifier><![CDATA[https://zbc.uz.zgora.pl/dlibra/publication/108329/edition/96416/content]]></dc:identifier>
<dc:identifier><![CDATA[oai:zbc.uz.zgora.pl:96416]]></dc:identifier>
<dc:source xml:lang="pl"><![CDATA[AMCS, volume 36, number 2 (2026)]]></dc:source>
<dc:source xml:lang="pl"><![CDATA[https://www.amcs.uz.zgora.pl/?action=papers&issue=140]]></dc:source>
<dc:language><![CDATA[eng]]></dc:language>
<dc:relation><![CDATA[oai:zbc.uz.zgora.pl:publication:108329]]></dc:relation>
<dc:rights xml:lang="pl"><![CDATA[Biblioteka Uniwersytetu Zielonogórskiego]]></dc:rights>
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