Complexity analysis of primal-dual interior-point methods for convex quadratic programming based on a new twice parameterized kernel function

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Bouhenache Youssra; Chikouche Wided; Touil Imene; Fathi Hafshejani Sajad

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Journal: Journal of Mathematical Modeling Year:2024 | Volume:12 | Issue:2 Page(s): 247-265

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Information Journal Paper

Title

Complexity analysis of primal-dual interior-point methods for convex quadratic programming based on a new twice parameterized kernel function

Author(s)

Bouhenache Youssra | Chikouche Wided | Touil Imene | Fathi Hafshejani Sajad | Issue Writer Certificate

Keywords

Convex quadratic programming

kernel function

Interior-point methods

Large- and small-update methods

Abstract

In this paper, we present primal-dual Interior-point methods (IPMs) for Convex quadratic programming (CQP) based on a new twice parameterized kernel function (KF) with a hyperbolic barrier term. To our knowledge, this is the first KF with a twice parameterized hyperbolic barrier term. By using some conditions and simple analysis, we derive the currently best-known iteration bounds for Large- and small-update methods, namely, $\textbf{O}\big(\sqrt{n}\log n\log\frac{n}{\epsilon}\big)$ and $\textbf{O}\big(\sqrt{n}\log\frac{n}{\epsilon}\big)$, respectively, with special choices of the parameters. Finally, some numerical results regarding the practical performance of the new proposed KF are reported.

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