A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization.

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Bibliographic Details
Title:	A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization.
Authors:	Bendaas, Yasmina¹ (AUTHOR) yasmina.bendaas@univ-setif.dz, Achache, Mohamed¹ (AUTHOR)
Source:	RAIRO: Operations Research (2804-7303). 2025, Vol. 59 Issue 6, p3505-3521. 17p.
Subjects:	Interior-point methods, Semidefinite programming, Polynomial time algorithms, Numerical analysis
Abstract:	In this paper, we present a theoretical and numerical study of a primal-dual path-following interior-point algorithm for solving convex quadratic semidefinite optimization problems (CQSDO). At each iteration, the algorithm uses only feasible full Nesterov-Todd steps for tracing approximately the central-path of CQSDO with the advantage that no line search is computed. Moreover, to ensure its well-definiteness and its locally quadratically convergence to an optimal solution and to enhance its numerical performances, new appropriate defaults are offered. Furthermore, we prove that the algorithm with short-update method has the currently best known polynomial complexity, namely, 풪(√(n+1)log(n/∊)). The efficiency of our algorithm is demonstrated through the numerical experiments on some CQSDO problems. Finally, a comparison between the efficiency of our proposed algorithm and existing ones is made. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

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Abstract:	In this paper, we present a theoretical and numerical study of a primal-dual path-following interior-point algorithm for solving convex quadratic semidefinite optimization problems (CQSDO). At each iteration, the algorithm uses only feasible full Nesterov-Todd steps for tracing approximately the central-path of CQSDO with the advantage that no line search is computed. Moreover, to ensure its well-definiteness and its locally quadratically convergence to an optimal solution and to enhance its numerical performances, new appropriate defaults are offered. Furthermore, we prove that the algorithm with short-update method has the currently best known polynomial complexity, namely, 풪(√(n+1)log(n/∊)). The efficiency of our algorithm is demonstrated through the numerical experiments on some CQSDO problems. Finally, a comparison between the efficiency of our proposed algorithm and existing ones is made. [ABSTRACT FROM AUTHOR]
ISSN:	28047303
DOI:	10.1051/ro/2025122