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arXiv · 2601.02797

Log-Polynomial Optimization

Jiyoung Choi·Jiawang Nie·Xindong Tang·Suhan Zhong
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Abstract

We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions including cross-entropy and Kullback-Leibler divergence. We propose a hierarchy of moment relaxations based on the truncated $K$-moment problems to solve log-polynomial optimization. We provide sufficient conditions for the hierarchy to be tight and introduce a numerical method to extract the global optimizers when the tightness is achieved. In addition, we modify relaxations with optimality conditions to better fit log-polynomial optimization with convenient Lagrange multipliers expressions. Various applications and numerical experiments are presented to show the efficiency of our method.

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Jiyoung Choi, Jiawang Nie, Xindong Tang, Suhan Zhong. 2026-01-06. Log-Polynomial Optimization. https://arxiv.org/abs/2601.02797

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