Connecting Max-entropy With Computational Geometry, LP And SDP
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915712903151616 |
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| author | Lasserre, Jean B |
| author_facet | Lasserre, Jean B |
| contents | We consider the well-known max-(relative) entropy problem $Θ$(y) = infQ$\ll$P DKL(Q P ) with Kullback-Leibler divergence on a domain $Ω$ $\subset$ R d , and with ''moment'' constraints h dQ = y, y $\in$ R m . We show that when m $\le$ d, $Θ$ is the Cram{é}r transform of a function v that solves a simply related computational geometry problem. Also, and remarkably, to the canonical LP: min x$\ge$0 {c T x\,: A x = y}, with A $\in$ R mxd , one may associate a max-entropy problem with a suitably chosen reference measure P on R d + and linear mapping h(x) = Ax, such that its associated perspective function $ε$ $Θ$(y/$ε$) is the optimal value of the log-barrier formulation (with parameter $ε$) of the dual LP (and so it converges to the LP optimal value as $ε$ $\rightarrow$ 0). An analogous result also holds for the canonical SDP: min X 0 { C, X\,: A(X) = y }. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03759 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Connecting Max-entropy With Computational Geometry, LP And SDP Lasserre, Jean B Optimization and Control We consider the well-known max-(relative) entropy problem $Θ$(y) = infQ$\ll$P DKL(Q P ) with Kullback-Leibler divergence on a domain $Ω$ $\subset$ R d , and with ''moment'' constraints h dQ = y, y $\in$ R m . We show that when m $\le$ d, $Θ$ is the Cram{é}r transform of a function v that solves a simply related computational geometry problem. Also, and remarkably, to the canonical LP: min x$\ge$0 {c T x\,: A x = y}, with A $\in$ R mxd , one may associate a max-entropy problem with a suitably chosen reference measure P on R d + and linear mapping h(x) = Ax, such that its associated perspective function $ε$ $Θ$(y/$ε$) is the optimal value of the log-barrier formulation (with parameter $ε$) of the dual LP (and so it converges to the LP optimal value as $ε$ $\rightarrow$ 0). An analogous result also holds for the canonical SDP: min X 0 { C, X\,: A(X) = y }. |
| title | Connecting Max-entropy With Computational Geometry, LP And SDP |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.03759 |