Sum of Squares and Polynomial Optimization

• S. Burgdorf, Kristijan Cafuta, Igor Klep, and Janez Povh.
  "Algorithmic aspects of sums of hermitian squares",
  Universität Konstanz, Fachbereich Mathematik und Statistik, Germany, November 2011.
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• A. A. Ahmadi and P. A. Parrilo.
  "A Complete Characterization of the Gap between Convexity and SOS-Convexity",
  Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, November 2011.
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• A. A. Ahmadi.
  "Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis",
  PhD Thesis; MIT; September, 2011.
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• Hayato Waki and Masakazu Muramatsu.
  "An extension of the elimination method for a sparse SOS polynomial",
  The University of Electro-Communications, Tokyo, Japan, September 2011.
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• J. Pena, J. Vera and L. Zuluaga.
  "Positive polynomials on unbounded equality-constrained domains",
  Working paper, Tepper School of Business, Carnegie Mellon University, May 2011.
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• D. Henrion and J. B. Lasserre.
  "Inner approximations for polynomial matrix inequalities and robust stability regions",
  LAAS-CNRS and Institute of Mathematics, Toulouse, France, Arpil 2011.
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• J. B. Lasserre.
  "A new look at nonnegativity on closed sets and polynomial optimization",
  LAAS-CNRS and Institute of Mathematics, Toulouse, France, Arpil 2011.
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• K. Cafuta, I. Klep and J. Povh.
  "Constrained Polynomial Optimization Problems with Noncommuting Variables",
  Manuscript, Insitute of mathematics, physics and mechanics, Slovenia, March 2011.
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• D. Henrion and F. Messine.
  "Finding largest small polygons with GloptiPoly",
  LAAS-CNRS Research Report, University of Toulouse, March 2011.
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• J. B. Lasserre.
  "Inverse polynomial optimization",
  LAAS-CNRS and Institute of Mathematics, University of Toulouse, LAAS, 7 avenue du Colonel Roche, 31077 Toulouse Cedex 4,France, March 2011.
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• A. A. Ahmadi, A. Olshevsky, P. A. Parrilo, and J. N. Tsitsiklis.
  "NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems",
  LIDS technical report 2855, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, December 2010.
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• E. de Klerk and M. Laurent.
  "On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems",
  Manuscript, Tilburg University, The Netherlands, November 2010.
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• M. Locatelli.
  "Convex envelopes for quadratic and polynomial functions over polytopes",
  Dipartimento di Ingegneria dell’Informazione, Universita di Parma, November 2010.
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• M. Laurent and P. Rostalski.
  "The Approach of Moments for Polynomial Equations",
  CWI, AMsterdam, August 2010. Written for the "Handbook of Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications" .
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• O. Devolde, F. Glineur and Y. Nesterov .
  "Solving Infinite-dimensional Optimization Problems by Polynomial Approximation ",
  CORE Discussion Paper 2010/29, Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Belgium, August 2010.
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• S. Burgdorf, K. Cafuta, I. Klep, and J. Povh.
  "Semidefinite programming certificates for tracial matrix inequalities",
  University of Konstanz, Germany, April 2010.
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• E. De Klerk and M. Laurent.
  "Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube",
  Preprint, Tilburg University, The Netherlands, April 2010.
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• J. B. Lasserre.
  "A 'joint+marginal' approach to parametric polynomial optimization",
  LAAS-CNRS, University of Toulouse, January 2010, to appear in SIAM J. Optim.
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• D. Papp, R. A. Collado and F Alizadeh.
  "Extension of the semidefinite characterization of sum of squares functional systems to algebraic structures",
  RUTCOR Research Report RRR 27-2009, Rutgers Center for Operations Research, Rutgers University, NJ, December 2009.
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• H. Waki and M. Muramatsu.
  "A Facial Reduction Algorithm for Finding Sparse SOS Representations",
  Technical Report CS-09-02, Department of Computer Science, The University of Electro-Communications, Tokyo, Novmeber 2009.
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• K. Cafuta, I. Klep, and J. Povh.
  "On the nonexistence of sum of squares certificates for the BMV conjecture",
  Insitute of mathematics, physics and mechanics, Slovenia, October 2009.
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• M. Laurent.
  "Sums of squares, moment matrices and optimization over polynomials",
  Emerging Applications of Algebraic Geometry, Vol. 149 of IMA Volumes in Mathematics and its Applications, M. Putinar and S. Sullivant (eds.), Springer, pages 157-270, 2009.
  Available on the homepage of Monique Laurent.
• I. Klep and J. Povh.
  "Semidefinite programming and sums of hermitian squares of noncommutative polynomials ",
  To appear in Journal of Pure and Applied Algebra; July 2009.
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• A. A. Ahmadi and P. A. Parrilo.
  "A convex polynomial that is not sos-convex",
  LIDS technical report #2810, March 2009.
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• S. Pironio, M. Navascues and A. Acin.
  "Convergent relaxations of polynomial optimization problems with non-commuting variables",
  Institute for Mathematical Sciences, Imperial College London, March 2009.
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• D. Bertsimas, X. V. Doan, J. Lasserre.
  "Optimal data fitting: a moment approach",
  Sloan School of Management, MIT, February 2007.
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• D. Bertsimas, X. V. Doan, J. Lasserre.
  "Multivariate exponential integral approximations: a moment approach",
  Sloan School of Management, MIT, January 2007.
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• J. Lasserre.
  "Sufficient Conditions for a Real Polynomial to be a Sum of Squares",
  Report #06789, LAAS, Toulouse, France. To appear in Archiv der Mathematik.
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• L. Jansson, J.B. Lasserre, C. Riener, T. Theobald.
  "Exploiting symmetries in SDP-relaxations for polynomial optimization",
  LAAS-report, September 2006, Toulouse, France.
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• Etienne De Klerk Gamal Elabwabi Dick Den Hertog .
  "Optimization of univariate functions on bounded intervals by interpolation and semidefinite programming",
  CentER Discussion paper 2006-26, Tilburg University, The Netherlands, April 2006..
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• A. Schürmann and F. Vallentin.
  "Computational Approaches to Lattice Packing and Covering Problems",
  University of Magedburg, June 2005.
  arXiv
• J. B. Lasserre.
  "Convergent SDP-relaxations in polynomial optimization with sparsity",
  Technical report #05-612, LAAS, Toulouse, France, April 2005; To appear in Siam J. Optimization .
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• M. Schweighofer.
  " Optimization of Polynomials on Compact Semialgebraic Sets",
  SIAM Journal on Optimization, Volume 15, Number 3, pp. 805-825, 2005.
  SIAM-Reference
• D. Henrion and J. B. Lasserre.
  "Convergent relaxations of polynomial matrix inequalities and static output feedback",
  LAAS-CNRS Research Report, November 2004.
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• E. de Klerk, M. Laurent, P. Parrilo.
  "A PTAS for the minimization of polynomials of fixed degree over the simplex",
  Preprint, March 2004, revised in October 2004.
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• H. Waki, S. Kim, M. Kojima and M. Muramatsu.
  "Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity",
  Research Report B-411, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152-8552, Japan, October 2004.
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• Masakazu Kojima and Masakazu Muramatsu.
  "An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems over Symmetric Cones",
  Research Report B-406, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan, April 2004.
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• J.B. Lasserre , T. Prieto-Rumeau.
  "SDP vs. LP relaxations for the moment approach in some performance evaluation problems",
  LAAS-CNRS, 31 077 Toulouse Cedex 4, France, April 2004. To appear in Stochastic Models.
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• Jean B. Lasserre.
  "A moment approach to analyze zeros of triangular polynomial sets",
  LAAS-CNRS, 31 077 Toulouse Cedex 4, France, March 2004.
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• D. Jibetean and M. Laurent.
  "Converging Semidefinite Bounds for Global Unconstrained Polynomial Optimization",
  CWI, Amsterdam, March 2004. Revised: January 2005.
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• Masakazu Kojima , Sunyoung Kim , Hayato Waki.
  "Sparsity in Sums of Squares of Polynomials",
  Research Report B-391, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, June 2003.
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• S. Kim, M. Kojima and H. Waki.
  "Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems",
  Research Report B-395, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, Sept./2003.
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• D. Jibetean and E.De Klerk.
  "Global optimization of rational functions: a semidefinite programming approach",
  CWI report, CWI, Amsterdam, The Netherlands, May 2003. .
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• L. Zuluaga , J. Vera , J. Pena.
  "LMI approximations for cones of positive semidefinite forms",
  GSIA Working Paper, Carnegie Mellon University, May 2003.
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• Z.-Q. Luo, J. F. Sturm and S. Zhang.
  "Multivariate Nonnegative Quadratic Mappings",
  Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, January 2003.
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• L. Zuluaga and J. Pena.
  "A Conic Programming Approach to Generalized Tchebycheff Inequalities",
  GSIA Working Paper, Carnegie Mellon University, 5000 Forbes Avenue Pittsburgh, PA 15213, October 2002. opt-online
• K. Gatermann and P.A. Parrilo.
  "Symmetry groups, semidefinite programs, and sums of squares",
  Journal of Pure and Appl. Algebra, Vol. 192, No. 1-3, pp. 95-128, 2004.
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• Paul Tseng. "Further Results on Approximating Nonconvex Quadratic Optimization by Semidefinite Programming Relaxation",
  Report, Department of Mathematics, University of Washington, Seattle, October 2001.
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• J. B. Lasserre. "SDP versus LP relaxations for polynomial programming",
  December 2001, to appear in Math. Oper. Res.
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• E. de Klerk and D.V. Pasechnik. "Products of positive forms, linear matrix inequalities, and Hilbert 17-th problem for ternary forms",
  Preprint, TU Delft, 2001.
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• P.A. Parrilo.
  "Semidefinite programming relaxations for semialgebraic problems",
  Mathematical Programming Ser. B, Vol. 96, No.2, pp. 293-320, 2003.
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• J. B. Lasserre.
  "Global optimization with polynomials and the problem of moments",
  SIAM J. Optim, Vol. 11 (2001), No. 3, pp. 796-817.
• Jean B. Lasserre.
  "Bounds on measures satisfying moment conditions",
  Technical report 00227; LAAS, Toulouse (France), June 2000. To appear in Annals of Applied Probability.
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