Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization
arXiv:1508.02068
Abstract
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming relaxations that grow tighter and tighter thanks to D'Angelo's and Putinar's Positivstellenstatz discovered in 2008. In other words, the Lasserre hierarchy may be transposed to complex numbers. We propose a method for exploiting sparsity and apply the complex hierarchy to problems with several thousand complex variables. These problems consist of computing optimal power flows in the European high-voltage transmission network.
30 pages, 5 tables, 4 figures
References in corpus (4)
Cited by in corpus (11)
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- A Component-Based Dual Decomposition Method for the OPF Problem
- Novel Approach Towards Global Optimality of Optimal Power Flow Using Quadratic Convex Optimization
- Counterexample to global convergence of DSOS and SDSOS hierarchies
- Computational Analysis of Sparsity-Exploiting Moment Relaxations of the OPF Problem
- Sparse polynomial interpolation: sparse recovery, super resolution, or Prony?
- Moment Relaxations of Optimal Power Flow Problems: Beyond the Convex Hull
- A Spatial Branch-and-Cut Method for Nonconvex QCQP with Bounded Complex Variables
- Approximation Algorithms for Optimization of Real-Valued General Conjugate Complex Forms