The Constant Trace Property in Noncommutative Optimization

2021/02/03 by Ngoc Hoang Anh, Abhishek Bhardwaj, Mai, Ngoc Hoang Anh +4
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2102.02162

openalex publication_date 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constant trace matrix variable. We then demonstrate how this constant trace property can be exploited via first order numerical methods to solve efficiently the semidefinite relaxations of the noncommutative problem.

Citations

• A Conditional Gradient-Based Augmented Lagrangian Framework

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