Exploiting Multistage Optimization Structure in Proximal Solvers

Fuente: arXiv
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Main Authors: Schwan, Roland, Kuhn, Daniel, Jones, Colin N.
Format: Preprint
Published: 2025
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author Schwan, Roland
Kuhn, Daniel
Jones, Colin N.
author_facet Schwan, Roland
Kuhn, Daniel
Jones, Colin N.
contents This paper presents an efficient structure-exploiting algorithm for multistage optimization problems. The proposed method extends existing approaches by supporting full coupling between stages and global decision variables in the cost, as well as equality and inequality constraints. The algorithm is implemented as a new backend in the PIQP solver and leverages a specialized block-tri-diagonal-arrow Cholesky factorization within a proximal interior-point framework to handle the underlying problem structure efficiently. The implementation features automatic structure detection and seamless integration with existing interfaces. Numerical experiments demonstrate significant performance improvements, achieving up to 13x speed-up compared to a generic sparse backend and matching/exceeding the performance of the state-of-the-art specialized solver HPIPM. The solver is particularly effective for applications such as model predictive control, robust scenario optimization, and periodic optimization problems.
format Preprint
id arxiv_https___arxiv_org_abs_2503_12664
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exploiting Multistage Optimization Structure in Proximal Solvers
Schwan, Roland
Kuhn, Daniel
Jones, Colin N.
Optimization and Control
Systems and Control
This paper presents an efficient structure-exploiting algorithm for multistage optimization problems. The proposed method extends existing approaches by supporting full coupling between stages and global decision variables in the cost, as well as equality and inequality constraints. The algorithm is implemented as a new backend in the PIQP solver and leverages a specialized block-tri-diagonal-arrow Cholesky factorization within a proximal interior-point framework to handle the underlying problem structure efficiently. The implementation features automatic structure detection and seamless integration with existing interfaces. Numerical experiments demonstrate significant performance improvements, achieving up to 13x speed-up compared to a generic sparse backend and matching/exceeding the performance of the state-of-the-art specialized solver HPIPM. The solver is particularly effective for applications such as model predictive control, robust scenario optimization, and periodic optimization problems.
title Exploiting Multistage Optimization Structure in Proximal Solvers
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2503.12664