Alternating direction method of multipliers for real and complex polynomial optimization models

References

• Li Z, He S, Zhang S. Approximation methods for polynomial optimization: models, algorithms, and applications. SpringerBriefs in optimization. New York (NY): Springer; 2012.
   Google Scholar
• Aubry A, De Maio A, Jiang B, Zhang S. Cognitive approach for ambiguity function shaping. Proceedings of the Seventh IEEE Sensor Array and Multichannel Signal Processing Workshop; 2012.
   Google Scholar
• Lasserre JB. Global optimization with polynomials and the problem of moments. SIAM J. Optim. 2001;11:796–817.
   Web of Science ®Google Scholar
• Parrilo PA. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization [PhD Dissertation]. Pasadena (CA): California Institute of Technology; 2000.
   Google Scholar
• Chen B, He S, Li Z, Zhang S. Maximum block improvement and polynomial optimization. SIAM J. Optim. 2012;22:87–107.
   Web of Science ®Google Scholar
• Chen B. Optimization with block variables: theory and applications [PhD Thesis]. Hong Kong: The Chinese University of Hong Kong; 2012.
   Google Scholar
• Douglas J, Rachford HH. On the numerical solution of the heat conduction problem in 2 and 3 space variables. Trans. Amer. Math. Soc. 1956;82:421–439.
   Google Scholar
• Yang J, Zhang Y. Alternating direction algorithms for ℓ1 problems in compressive sensing. SIAM J. Sci. Comput. 2011;33:250–278.
   Web of Science ®Google Scholar
• Wang Y, Yang J, Yin W, Zhang Y. A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 2008;1:248–272.
   Web of Science ®Google Scholar
• Goldstein T, Osher S. The split Bregman method for L1-regularized problems. SIAM J. Imag. Sci. 2009;2:323–343.
   Web of Science ®Google Scholar
• Tao M, Yuan X. Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J. Optim. 2011;21:57–81.
   Web of Science ®Google Scholar
• Ma S. Alternating direction method of multipliers for sparse principal component analysis. J Oper. Res. Soc. China. 2013;1:253–274.
   Google Scholar
• Wen Z, Goldfarb D, Yin W. Alternating direction augmented Lagrangian methods for semidefinite programming. Math. Program. Comput. 2010;2:203–230.
   Google Scholar
• Boyd S, Parikh N, Chu E, Peleato B, Eckstein J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 2011;3:1–122.
   Google Scholar
• Xu Y, Yin W, Wen Z, Zhang Y. An alternating direction algorithm for matrix completion with nonnegative factors. J. Front. Math. China Special Issues Comput. Math. 2011;365–384.
   Google Scholar
• Jiang B, Li Z, Zhang S. Conjugate symmetric complex tensors and applications. Working Paper; 2013.
   Google Scholar
• Lim L-H. Singular values and eigenvalues of tensors: a variational approach. In: Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 05); 2005; Puerto Vallarta, Mexico. p. 129–132.
   Google Scholar
• Qi L. Eigenvalues of a real supersymmetric tensor. J. Symb. Comput. 2005;40:1302–1324.
   Web of Science ®Google Scholar
• Qi L, Wang F, Wang Y. Z-eigenvalue methods for a global polynomial optimization problem. Math. Program. Ser. A. 2009;118:301–316.
   Web of Science ®Google Scholar
• Kofidis E, Regalia PA. On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM J. Matrix Anal. Appl. 2002;23:863–884.
   Web of Science ®Google Scholar
• Kolda TG, Mayo JR. Shifted power method for computing tensor eigenpairs. SIAM J. Mat. Anal. 2011;32:1095–1124.
   Web of Science ®Google Scholar
• Jiang B, Ma S, Zhang S. Tensor principal component analysis via convex optimization. Working Paper; 2012.
   Google Scholar
• Gabay D. Applications of the method of multipliers to variational inequalities. In: Fortin M, Glowinski R, editors. Augmented Lagrangian methods: applications to the solution of boundary value problems. Amsterdam: North-Holland; 1983.
   Google Scholar
• Eckstein J, Bertsekas DP. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 1992;55:293–318.
   Web of Science ®Google Scholar
• Henrion D, Lasserre JB, Loefberg J. GloptiPoly 3: moments, optimization and semidefinite programming. Optim. Meth. Softw. 2009;24:761–779.
   Web of Science ®Google Scholar