Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization

By Cédric Josz, Daniel D. Molzahn. 2015

47 citations recorded by the source corpus.

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.

Subfields: Electrical and Electronic Engineering, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/60371b42d869240aee87455a4a1a967fcfe81cff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

  1. K. Sundar
  2. Russell W. Bent
  3. Carleton Coffrin
  4. Yeesian Ng
  5. Miles Lubin
  6. Steven H. Low

In Numerical Analysis

  1. Russell W. Bent
  2. Miles Lubin

In Statistics and Probability

  1. Carleton Coffrin
  2. Miles Lubin

Citations in the corpus