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In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization problems (POPs) and purports that this refutes claims in our extended abstract [4] and slides in [3].
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
P. A. Parrilo · 2000
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On the equivalence of algebraic approaches to the minimization of forms on the simplex
E. de Klerk, M. Laurent, and P. Parrilo · 2005
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Moments, Positive Polynomials and Their Applications
J. B. Lasserre · 2009
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Copositive Programming
S. Burer · 2012
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DSOS and SDSOS: More tractable alternatives to SOS
A. A. Ahmadi and A. Majumdar · 2013
Earlier work this paper cites.
DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization
A. A. Ahmadi and A. Majumdar · 2014
Cited alongside, same era.
Control and verification of high-dimensional systems with DSOS and SDSOS programming
A. Majumdar, A. Ahmadi, and R. Tedrake · 2014
Cited alongside, same era.
Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone
F. Permenter and P. Parrilo · 2014
Cited alongside, same era.
An Introduction to Polynomial and Semialgebraic Optimization
J. B. Lasserre · 2015
Cited alongside, same era.
A. A. Ahmadi and G. Hall · 2017
Cited alongside, same era.
Sum of squares basis pursuit with linear and second order cone programming
A. A. Ahmadi and G. Hall · 2017
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A. A. Ahmadi and A. Majumdar · 2017
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Counterexample to global convergence of DSOS and SDSOS hierarchies
C. Josz · 2017
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Alternative SDP and SOCP approximations for polynomial optimization
X. Kuang, B. Ghaddar, J. Naoum-Sawaya, and L. Zuluaga · 2017
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Positive polynomials on unbounded domains
J. Peña, J. Vera, and L. Zuluaga · 2017
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