Laouar, Mounia ; Brahimi, Mahmoud ; Ziadi, Raouf ; Saleh, Mohammed A. ; Almaymuni, Abdulgader Z. ; Alhalangy, Abdalilah
Contributor:Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Title:A primal-dual interior point method for complex-variable optimization problems
Group publication title: Subject and Keywords:convex optimization ; complex variables ; optimization problems ; complex-valued kernel function ; Newton direction
Abstract: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. ; 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. ; 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.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 36, number 2 (2026) ; click here to follow the link
Language: License CC BY 4.0: Rights: