Theory and applications of the Sum-Of-Squares technique
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913259397840896 |
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| author | Bach, Francis Cornacchia, Elisabetta Pesce, Luca Piccioli, Giovanni |
| author_facet | Bach, Francis Cornacchia, Elisabetta Pesce, Luca Piccioli, Giovanni |
| contents | The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using reproducing kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_16255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theory and applications of the Sum-Of-Squares technique Bach, Francis Cornacchia, Elisabetta Pesce, Luca Piccioli, Giovanni Optimization and Control Information Theory Statistics Theory The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using reproducing kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function. |
| title | Theory and applications of the Sum-Of-Squares technique |
| topic | Optimization and Control Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2306.16255 |