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arXiv · 2012.08873

Exploiting constant trace property in large-scale polynomial optimization

Ngoc Hoang Anh Mai·Jean-Bernard Lasserre·Victor Magron·Jie Wang
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Abstract

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such moment relaxations can be solved efficiently by first-order methods that exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. We also extend this CTP-exploiting framework to large-scale POPs with different sparsity structures. The efficiency and scalability of our framework are illustrated on second-order moment relaxations for various randomly generated quadratically constrained quadratic programs.

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Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron, Jie Wang. 2020-12-16. Exploiting constant trace property in large-scale polynomial optimization. https://arxiv.org/abs/2012.08873

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