GPU Implementation of Second-Order Linear and Nonlinear Programming Solvers
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912723815628800 |
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| author | Montoison, Alexis Pacaud, François Shin, Sungho Anitescu, Mihai |
| author_facet | Montoison, Alexis Pacaud, François Shin, Sungho Anitescu, Mihai |
| contents | In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS. This paper provides an overview of the state of the art in GPU-based second-order solvers, focusing on pivoting-free interior-point methods for large and sparse linear and nonlinear programs. We begin by highlighting the capabilities and limitations of the currently available GPU-accelerated sparse linear solvers. Next, we discuss different formulations of the Karush-Kuhn-Tucker systems for second-order methods and evaluate their suitability for pivoting-free GPU implementations. We also discuss strategies for computing sparse Jacobians and Hessians on GPUs for nonlinear programming. Finally, we present numerical experiments demonstrating the scalability of GPU-based optimization solvers. We observe speedups often exceeding 10x compared to comparable CPU implementations on large-scale instances when solved up to medium precision. Additionally, we examine the current limitations of existing approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_16094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GPU Implementation of Second-Order Linear and Nonlinear Programming Solvers Montoison, Alexis Pacaud, François Shin, Sungho Anitescu, Mihai Optimization and Control In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS. This paper provides an overview of the state of the art in GPU-based second-order solvers, focusing on pivoting-free interior-point methods for large and sparse linear and nonlinear programs. We begin by highlighting the capabilities and limitations of the currently available GPU-accelerated sparse linear solvers. Next, we discuss different formulations of the Karush-Kuhn-Tucker systems for second-order methods and evaluate their suitability for pivoting-free GPU implementations. We also discuss strategies for computing sparse Jacobians and Hessians on GPUs for nonlinear programming. Finally, we present numerical experiments demonstrating the scalability of GPU-based optimization solvers. We observe speedups often exceeding 10x compared to comparable CPU implementations on large-scale instances when solved up to medium precision. Additionally, we examine the current limitations of existing approaches. |
| title | GPU Implementation of Second-Order Linear and Nonlinear Programming Solvers |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.16094 |