Autor:

Laouar, Mounia ; Brahimi, Mahmoud ; Ziadi, Raouf ; Saleh, Mohammed A. ; Almaymuni, Abdulgader Z. ; Alhalangy, Abdalilah

Współtwórca:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Tytuł:

A primal-dual interior point method for complex-variable optimization problems

Tytuł publikacji grupowej:

AMCS, volume 36 (2026)

Temat i słowa kluczowe:

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.

Wydawca:

Zielona Góra: Uniwersytet Zielonogórski

Data wydania:

2026

Typ zasobu:

artykuł

DOI:

10.61822/amcs-2026-0013

Strony:

177-194

Źródło:

AMCS, volume 36, number 2 (2026) ; kliknij tutaj, żeby przejść

Jezyk:

eng

Licencja CC BY 4.0:

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Prawa do dysponowania publikacją:

Biblioteka Uniwersytetu Zielonogórskiego