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In a recent note [8], the author provides a counterexample to the globalconvergence of what his work refers to as "the DSOS and SDSOS hierarchies" forpolynomial optimization problems (POPs) and purports that this refutes claimsin our extended abstract [4] and slides in [3]. The goal of this paper is toclarify that neither [4], nor [3], and certainly not our full paper [5], everdefined DSOS or SDSOS hierarchies as it is done in [8]. It goes without sayingthat no claims about convergence properties of the hierarchies in [8] were evermade as a consequence. What was stated in [4,3] was completely different: westated that there exist hierarchies based on DSOS and SDSOS optimization thatconverge. This is indeed true as we discuss in this response. We also emphasizethat we were well aware that some (S)DSOS hierarchies do not converge even iftheir natural SOS counterparts do. This is readily implied by an example in ourprior work [5], which makes the counterexample in [8] superfluous. Finally, weprovide concrete counterarguments to claims made in [8] that aim to challengethe scalability improvements obtained by DSOS and SDSOS optimization ascompared to sum of squares (SOS) optimization.  [3] A. A. Ahmadi and A. Majumdar. DSOS and SDSOS: More tractable alternativesto SOS. Slides at the meeting on Geometry and Algebra of Linear MatrixInequalities, CIRM, Marseille, 2013. [4] A. A. Ahmadi and A. Majumdar. DSOS andSDSOS optimization: LP and SOCP-based alternatives to sum of squaresoptimization. In proceedings of the 48th annual IEEE Conference on InformationSciences and Systems, 2014. [5] A. A. Ahmadi and A. Majumdar. DSOS and SDSOSoptimization: more tractable alternatives to sum of squares and semidefiniteoptimization. arXiv:1706.02586, 2017. [8] C. Josz. Counterexample to globalconvergence of DSOS and SDSOS hierarchies. arXiv:1707.02964, 2017.

Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies"