Optimal Preconditioning for Online Quadratic Cone Programming
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909595318878208 |
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| author | Kamath, Abhinav G. Elango, Purnanand Açıkmeşe, Behçet |
| author_facet | Kamath, Abhinav G. Elango, Purnanand Açıkmeşe, Behçet |
| contents | First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere preconditioner--for a class of quadratic cone programs (QCPs), i.e., conic optimization problems with a quadratic objective function, wherein the objective function is strongly convex and possesses a certain structure. This approach lends itself to factorization-free, customizable, first-order conic optimization for online applications wherein the solver is called repeatedly to solve problems of the same size/structure, but with changing problem data. We demonstrate the efficacy of our approach on numerical convex and nonconvex trajectory optimization examples, using a first-order conic optimizer under the hood. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Preconditioning for Online Quadratic Cone Programming Kamath, Abhinav G. Elango, Purnanand Açıkmeşe, Behçet Optimization and Control First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere preconditioner--for a class of quadratic cone programs (QCPs), i.e., conic optimization problems with a quadratic objective function, wherein the objective function is strongly convex and possesses a certain structure. This approach lends itself to factorization-free, customizable, first-order conic optimization for online applications wherein the solver is called repeatedly to solve problems of the same size/structure, but with changing problem data. We demonstrate the efficacy of our approach on numerical convex and nonconvex trajectory optimization examples, using a first-order conic optimizer under the hood. |
| title | Optimal Preconditioning for Online Quadratic Cone Programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.14191 |