Finite convergence of the Moment-SOS hierarchy under hidden convexity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915824346857472 |
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| author | Ðurašinović, Srećko Lasserre, Jean B. |
| author_facet | Ðurašinović, Srećko Lasserre, Jean B. |
| contents | One considers polynomial optimization problems with compact feasible set $\mathbfΩ$ defined by SOS-concave polynomials $g_j$, and with a globally non-convex polynomial objective $f$. We show that if $f$ is strongly convex on $\mathbfΩ$, or SOS-convex on $\mathbfΩ$ when the constraints $g_j$ are at most quadratic, then the associated Moment-SOS hierarchy converges in finitely many steps, without à priori knowledge of this hidden (local) convexity. In addition, in the latter case, the exact order for which the relaxation is exact is
provided by the degree of a Putinar-like certificate of convexity. This demonstrates that a general-purpose hierarchy can adapt to favorable hidden properties of a specific instance without being informed of them, yielding certified global minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite convergence of the Moment-SOS hierarchy under hidden convexity Ðurašinović, Srećko Lasserre, Jean B. Optimization and Control One considers polynomial optimization problems with compact feasible set $\mathbfΩ$ defined by SOS-concave polynomials $g_j$, and with a globally non-convex polynomial objective $f$. We show that if $f$ is strongly convex on $\mathbfΩ$, or SOS-convex on $\mathbfΩ$ when the constraints $g_j$ are at most quadratic, then the associated Moment-SOS hierarchy converges in finitely many steps, without à priori knowledge of this hidden (local) convexity. In addition, in the latter case, the exact order for which the relaxation is exact is provided by the degree of a Putinar-like certificate of convexity. This demonstrates that a general-purpose hierarchy can adapt to favorable hidden properties of a specific instance without being informed of them, yielding certified global minimizers. |
| title | Finite convergence of the Moment-SOS hierarchy under hidden convexity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.00284 |