215. Proximal Augmented Lagrangian Regularization: A Primal-Dual Modular Interior-Point QP Solver.
Invited abstract in session WB-11: Interior point methods and applications - Part I, stream Interior point methods and applications.
Wednesday, 10:30-12:30Room: B100/5017
Authors (first author is the speaker)
| 1. | Jeremy Bertoncini
|
| Institute of Applied Mathematics, University of the Bundeswehr Munich | |
| 2. | Alberto De Marchi
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| University of the Bundeswehr Munich | |
| 3. | Matthias Gerdts
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| Institut fur Mathematik und Rechneranwendung, Universitat der Bundeswehr Munchen |
Abstract
Quadratic Programming (QP) problems are fundamental in many fields such as optimization, machine learning or control theory. Our research introduces an interior point (IP) primal-dual solver that leverages both proximal and augmented Lagrangian regularization techniques, to efficiently address QP optimization problems. By combining the proximal regularization technique for higher convexity and the augmented Lagrangian method for enforcing inequality and equality constraints, the approach effectively balances computational efficiency with solution accuracy. Introduced in a suitable merit function, the convexified proximal sub-problem is iteratively solved using an inexact linesearch having conditions on both primal and dual variables. To further improve robustness, IP-slack variables are regularized ensuring a stable handling of the log-barrier term resulting into improved convergence properties. The solver integrates such methods to handle redundant linear constraints and achieve superlinear convergence properties. Additionally, the solver is object-oriented and modular, including multiple linesearch conditions, KKT-schemes, and termination strategies, allowing for greater flexibility and adaptability in different optimization scenarios. The numerical experiments demonstrate the solver’s effectiveness in tackling the Maros-Mészáros Testset, showcasing its ability to achieve high precision even with ill-conditioned, redundant constraints and badly scaled problems.
Keywords
- Computational mathematical optimization
- Optimization software
- Linear and nonlinear optimization
Status: accepted
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