Discussion on:'A Decomposition Algorithm for KYP-SDPs'

摘要

The paper by Falkeborn-Hansson is an interesting contribution discussing decomposition of a semidefinite programming problem produced by the KYP lemma. In particular, the authors consider a semidefinite programming problem with several local constraints including only subsets of variables and with one complicating constraint including all the variables. If the complicating constraint did not exist, the problem could be decomposed into several subproblems solvable independently. This is actually carried out by considering the Lagrange relaxation of the given problem and optimizing the Lagrange multiplier of the complicating constraint. Although iteration is necessary for optimization of the Lagrange multiplier, the overall computational time is reduced if each produced subproblem is solved fast enough. This benefit is clearly shown bv the presented example.