Inexact log-domain interior-point methods for quadratic programming

Jordan Leung (), Frank Permenter () and Ilya Kolmanovsky ()
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Jordan Leung: University of Michigan
Frank Permenter: Toyota Research Institute
Ilya Kolmanovsky: University of Michigan

Computational Optimization and Applications, 2024, vol. 89, issue 3, No 3, 625-658

Abstract: Abstract This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework. In a set of computational experiments, the inexact LDIPMs demonstrate a 24–72% reduction in the total number of CG iterations required for termination relative to implementations with a fixed termination tolerance. This translates into an important computation time reduction in applications such as real-time optimization and model predictive control.

Keywords: Quadratic programming; Interior-point methods; Inexact Newton methods; Iterative methods for linear systems (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00610-7

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