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Exploiting constant trace property in large-scale polynomial optimization

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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Preprints, Working Papers, ...
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https://hal.laas.fr/hal-03079000
Contributor : Victor Magron <>
Submitted on : Thursday, December 17, 2020 - 8:19:16 AM
Last modification on : Thursday, June 10, 2021 - 3:07:14 AM

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  • HAL Id : hal-03079000, version 1
  • ARXIV : 2012.08873

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Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron, Jie Wang. Exploiting constant trace property in large-scale polynomial optimization. 2020. ⟨hal-03079000⟩

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