Pablo's homepage

Preprints
Book chapters
Journal articles
PhD Thesis
Conference papers

If you do not have access to the online version of a paper, please feel free to email me.

Preprints

• New lower bounds on nonnegative rank using conic programming
  H. Fawzi, P.A. Parrilo
  http://arxiv.org/abs/1210.6970
  
• Polynomial-sized Semidefinite Representations of Derivative Relaxations of Spectrahedral Cones
  J. Saunderson, P.A. Parrilo
  http://arxiv.org/abs/1208.1443
  
• Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
  J. Saunderson, V. Chandrasekaran, P.A. Parrilo, and A. Willsky
  http://arxiv.org/abs/1204.1220
  
• An optimal controller architecture for poset-causal systems
  P. Shah and P.A. Parrilo,
  http://arxiv.org/abs/1111.7221
  
• A complete characterization of the gap between convexity and SOS-convexity
  A.A. Ahmadi and P.A. Parrilo,
  http://arxiv.org/abs/1111.4587
  
• Lifts of convex sets and cone factorizations
  J. Gouveia, P.A. Parrilo, and R. Thomas
  http://arxiv.org/abs/1111.3164
  
• Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
  A.A. Ahmadi, R. Jungers, P.A. Parrilo, and M. Roozbehani
  http://arxiv.org/abs/1111.3427
  
• H₂-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback
  P. Shah, P.A. Parrilo
  http://arxiv.org/abs/1111.1498
  
• Dynamics in near-potential games
  O. Candogan, A. Ozdaglar, P.A. Parrilo
  http://arxiv.org/abs/1107.4386
  
• NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems
  A.A. Ahmadi, A. Olshevsky, P.A. Parrilo, J.N. Tsitsiklis
  http://arxiv.org/abs/1012.1908
  
• Convex Graph Invariants
  V. Chandrasekaran, P.A. Parrilo, and A.S. Willsky
  http://arxiv.org/abs/1012.0623
  
• The Convex Geometry of Linear Inverse Problems
  V. Chandrasekaran, B. Recht, P.A. Parrilo, and A.S. Willsky
  http://arxiv.org/abs/1012.0621
  
• Latent Variable Graphical Model Selection via Convex Optimization
  V. Chandrasekaran, P.A. Parrilo, and A.S. Willsky
  http://arxiv.org/abs/1008.1290
  
• A new proof of Nash's Theorem via exchangeable equilibria
  N. Stein, P.A. Parrilo and A. Ozdaglar
  http://arxiv.org/abs/1005.3045
  
• Flows and Decompositions of Games: Harmonic and Potential Games
  O. Candogan, I. Menache, A. Ozdaglar and P. A. Parrilo
  http://arxiv.org/abs/1005.2405
  
• A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs
  J. Gouveia, M. Laurent, P.A. Parrilo and R. Thomas
  http://arxiv.org/abs/0907.4518
  
• A convex polynomial that is not sos-convex
  A. A. Ahmadi and P.A. Parrilo
  http://arxiv.org/abs/0903.1287
  
• Polynomial stochastic games via sum of squares optimization
  P. Shah and P.A. Parrilo
  http://arxiv.org/abs/0806.2469
  
• An explicit construction of distinguished representations of polynomials nonnegative over finite sets
  P.A. Parrilo,
  IfA Technical Report AUT02-02, March 2002.
  

Book chapters

• Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization
  J.A. De Loera, P.N. Malkin and P.A. Parrilo
  In Mixed Integer Nonlinear Programming,
  IMA Volumes in Mathematics and its Applications, Volume 154, Part 7, 447-481. J. Lee, S. Leyffer (Eds.), 2012. http://arxiv.org/abs/0909.0808
  DOI
• Semidefinite Representation of the k-Ellipse
  J. Nie, P.A. Parrilo and B. Sturmfels
  In Algorithms in Algebraic Geometry,
  IMA Volumes in Mathematics and its Applications, Vol. 146, A. Dickenstein, F.-O. Schreyer, A.J. Sommese (Eds.), Springer, 2008.
  http://arxiv.org/abs/math.AG/0702005
  
• Exploiting algebraic structure in sum of squares programs
  P.A. Parrilo,
  In Positive polynomials in Control,
  Lecture Notes in Control and Information Sciences, Vol. 312, pp. 181--194, Springer, 2005. DOI
• On the equivalence of algebraic approaches to the minimization of forms on the simplex
  E. de Klerk, M. Laurent, P.A. Parrilo,
  In Positive polynomials in Control,
  Lecture Notes in Control and Information Sciences, Vol. 312, pp. 121--132, Springer, 2005. DOI
• SOSTOOLS and its Control applications
  S. Prajna, A. Papachristodoulou, P. Seiler, P.A. Parrilo,
  In Positive polynomials in Control,
  Lecture Notes in Control and Information Sciences, Vol. 312, pp. 273--292, Springer, 2005. DOI
• Minimizing polynomial functions
  P.A. Parrilo, B. Sturmfels,
  In Algorithmic and quantitative real algebraic geometry,
  DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 60, pp. 83--99, AMS.
  http://www.arxiv.org/abs/math.OC/0103170
  

Journal articles

• Structure of Extreme Correlated Equilibria
  N. Stein, A. Ozdaglar and P.A. Parrilo
  International Journal of Game Theory, Volume 40, Number 4, 749-767, 2011. DOI
  http://arxiv.org/abs/1002.0035
  
• Design of Photonic Crystals with Multiple and Combined Band Gaps
  H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire
  Physical Review E, Vol. 83, Issue 4, 2011. DOI
  Full text version
  
• Rank-Sparsity Incoherence for Matrix Decomposition
  V. Chandrasekaran, S. Sanghavi, P.A. Parrilo and A. Willsky
  SIAM Journal on Optimization, Vol. 21, Issue 2, pp. 572-596, 2011. DOI
  http://arxiv.org/abs/0906.2220
  
• Correlated Equilibria in Continuous Games: Characterization and Computation
  N. Stein, P.A. Parrilo and A. Ozdaglar
  Games and Economic Behavior, Vol. 71, No. 2, pp. 436-455 (2011). DOI
  http://arxiv.org/abs/0812.4279
  
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
  B. Recht, M. Fazel and P.A. Parrilo
  SIAM Review, Vol. 52, Issue 3, pp. 471-501 (2010). DOI
  http://arxiv.org/abs/0706.4138
  final pdf.
  
• Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods
  H. Men, N.-C. Nguyen, R.M. Freund, P.A. Parrilo and J. Peraire
  Journal of Computational Physics, Vol. 229 (2010) pp. 3706-3725. DOI
  http://arxiv.org/abs/0907.2267
  
• Optimality of Affine Policies in Multi-stage Robust Optimization
  D. Bertsimas, D.A. Iancu and P.A. Parrilo
  Mathematics of Operations Research, Vol. 35, No. 2, May 2010, pp. 363-394. DOI
  http://arxiv.org/abs/0904.3986
  
• Theta Bodies for Polynomial Ideals
  J. Gouveia, P.A. Parrilo, and R. Thomas
  SIAM J. Optim., Vol. 20, Issue 4, pp. 2097-2118, 2010. DOI
  http://arxiv.org/abs/0809.3480
  
• Constrained Consensus and Optimization in Multi-Agent Networks
  A. Nedic, A. Ozdaglar and P.A. Parrilo
  IEEE Transactions on Automatic Control, Vol. 55, Issue 4, pp. 922-938, 2010. DOI
  http://arxiv.org/abs/0802.3922
  
• Fastest mixing Markov chain on graphs with symmetries
  S. Boyd, P. Diaconis, P.A. Parrilo and L. Xiao
  SIAM Journal on Optimization, Vol. 20, Issue 2, pp. 792-819, 2009. DOI
  http://arxiv.org/abs/0709.0955
  
• Computing sum of squares decompositions with rational coefficients
  H. Peyrl and P.A. Parrilo
  Theoretical Computer Science, Vol. 409, Issue 2, pp. 269-281 (2008). DOI
  
• Separable and Low-Rank Continuous Games
  N. Stein, A. Ozdaglar and P.A. Parrilo
  International Journal of Game Theory, Vol. 37, No. 4, pp. 457-474, 2008. DOI
  http://arxiv.org/abs/0707.3462
  
• On the asymptotic minimum number of monochromatic 3-term arithmetic progressions
  P. A. Parrilo, A. Robertson and D. Saracino
  Journal of Combinatorial Theory, Series A, Vol. 115, No. 1, pp. 185-192, 2008. DOI
  http://arxiv.org/abs/math.CO/0609532
  
• Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming
  E. M. Aylward, P. A. Parrilo, J.-J. E. Slotine
  Automatica, Vol. 44, No. 8, pp. 2163--2170, 2008. DOI
  http://arxiv.org/abs/math.OC/0603313
  
• Structured semidefinite programs for the control of symmetric systems
  R. Cogill, S. Lall and P.A. Parrilo,
  Automatica, Vol. 44, No. 5, pp. 1411--1417, 2008. DOI
  
• Approximation of the joint spectral radius using sum of squares
  P.A. Parrilo and A. Jadbabaie
  Linear Algebra and its Applications, Vol. 428, No. 10, pp. 2385--2402, 2008. DOI
  http://arxiv.org/abs/0712.2887
• Efficient classification of complete parameter regions based on semidefinite programming
  L. Kuepfer, U. Sauer and P.A. Parrilo
  BMC Bioinformatics, Vol. 8, No. 12, 2007.
  http://dx.doi.org/10.1186/1471-2105-8-12
  
• Improved quantum algorithms for the ordered search problem via semidefinite programming
  A. M. Childs and A. J. Landahl and P. A. Parrilo, Phys. Rev. A, Vol. 75, 032335, 2007. DOI
  http://arxiv.org/abs/quant-ph/0608161
  
• Parametric optimization and optimal control using algebraic geometry methods
  I. A. Fotiou, P. Rostalski, P. A. Parrilo, and M. Morari, International Journal of Control, Vol. 79, No. 11, 2006. DOI
  pdf.
• Symmetry analysis of reversible Markov chains
  S. Boyd, P. Diaconis, P.A. Parrilo and L. Xiao, Internet Mathematics, Vol 2, No. 1, 2005.
  pdf.
• A PTAS for the minimization of polynomials of fixed degree over the simplex
  E. de Klerk, M. Laurent, P.A. Parrilo, Theoretical Computer Science, Volume 361, pp. 210-225, 2006. DOI
  pdf.
  
• The Lax conjecture is true
  A.S. Lewis, P.A. Parrilo, M.V. Ramana, Proceedings of the AMS, Vol. 133, pp. 2495-2499, 2005. DOI
  http://www.arxiv.org/abs/math.OC/0304104
  
• Detecting multipartite entanglement
  A.C. Doherty, P.A. Parrilo, and F. Spedalieri, Phys. Rev. A, Vol. 71, 032333, 2005. DOI
  http://www.arxiv.org/abs/quant-ph/0407143
  
• Symmetry groups, semidefinite programs, and sums of squares
  K. Gatermann, P.A. Parrilo, Journal of Pure and Appl. Algebra, Vol. 192, No. 1-3, pp. 95-128, 2004. DOI
  http://www.arxiv.org/abs/math.AC/0211450
  
• Robust identification toolbox
  M.C. Mazzaro, P.A. Parrilo, R.S. Sánchez Peña, Latin American Applied Research, Vol. 34, No. 2, pp. 91-100, 2004.
• Nonlinear control synthesis by convex optimization
  S. Prajna, P.A. Parrilo, A. Rantzer, IEEE Transactions on Automatic Control, Vol. 49, No. 2, 2004 DOI
  Abstract, pdf
  
• An inequality for circle packings proved by semidefinite programming
  P.A. Parrilo, R. Peretz, Discrete and Computational Geometry, Vol. 31, No. 3, 2004. DOI
  http://www.arxiv.org/abs/math.AG/0205278
  
• A complete family of separability criteria
  A. C. Doherty, P.A. Parrilo, F. M. Spedalieri, Phys. Rev. A, Vol. 69, 022308, 2004. DOI
  http://www.arxiv.org/abs/quant-ph/0308032
  
• Semidefinite programming relaxations and algebraic optimization in Control
  P.A. Parrilo, S. Lall, European Journal of Control, Vol. 9, No. 2-3, 2003.
  Abstract, pdf, postscript, gzipped postscript.
  
• Semidefinite programming relaxations for semialgebraic problems.
  P.A. Parrilo, Mathematical Programming Ser. B, Vol. 96, No.2, pp. 293-320, 2003. DOI
  Abstract, pdf, postscript, gzipped postscript.
  
• Distinguishing separable and entangled states
  A.C. Doherty, P.A. Parrilo, F.M. Spedalieri, Physical Review Letters, Vol. 88, No. 18, 2002. DOI
  http://www.arxiv.org/abs/quant-ph/0112007
  
• A Convex Approach to Robust $\mathcal{H}_2$ Performance Analysis
  M. Sznaier, T. Amishima, P.A. Parrilo, J. Tierno, Automatica, Vol. 38, No. 6, pp. 957-966, 2002. DOI
  
• Robust identification: an approach to select the class of candidate models
  M.C. Mazzaro, P.A. Parrilo, R.S. Sánchez Peña, Int. J. Control, Vol. 74, No. 12, pp. 1210-1218, 2001. DOI
  
• Robust identification with mixed parametric/nonparametric models and time/frequency-domain experiments: Theory and an application
  T. Inanc, M. Sznaier, P.A. Parrilo, R. S. Sánchez Peña, IEEE Transactions on Control Systems Technology, Vol. 9, No. 4, 2001. DOI
  
• On Cone-Invariant Linear Matrix Inequalities
  P.A. Parrilo, S. Khatri, IEEE Transactions on Automatic Control, Vol. 45, No. 8, 2000. DOI
  
• A parametric extension of mixed time/frequency robust identification
  P.A. Parrilo, R.S. Sánchez Peña, M. Sznaier, IEEE Transactions on Automatic Control, Vol. 44, No. 2, 1999. DOI
  
• Mixed time/frequency-domain based robust identification
  P.A. Parrilo, M. Sznaier, R. S. Sánchez Peña, T. Inanc, Automatica, Vol. 34, No. 11, 1998. DOI
  
• L_1 Identification Applied to a Fluid Dynamics Problem
  P.A. Parrilo, R. S. Sánchez Peña, C. G. Galarza, IEEE Transactions on Control Systems Technology, Vol. 4, No. 3, 1996. DOI
  

PhD Thesis

• Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
  California Institute of Technology, Pasadena, CA, May 2000.
  Abstract, postscript, gzipped postscript, pdf.
  Official version (Caltech ETD)

Conference papers

• P.A. Parrilo, Polynomial games and sum of squares optimization, Proceedings for the 45th IEEE Conference on Decision and Control, pp. 2855 - 2860, 2006. DOI final pdf.
  
• S. Prajna, A. Papachristodoulou, P. Seiler, P.A. Parrilo, SOSTOOLS: Control applications and new developments, 2004 IEEE International Symposium on Computer Aided Control Systems Design, pp. 315 - 320, 2004. DOI
  
• P.A. Parrilo, Exploiting structure in sum of squares programs, Proceedings for the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003. DOI
  
• P. Grieder, P.A. Parrilo, M. Morari, Robust Receding Horizon Control - Analysis and Synthesis, Proceedings for the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003. DOI
  
• H. Anai, P.A. Parrilo, Convex Quantifier Elimination for Semidefinite Programming, Proceedings of the International Workshop on Computer Algebra in Scientific Computing (CASC 2003), 2003. pdf
• R. Cogill, S. Lall, P.A. Parrilo, On structured semidefinite programs for the control of symmetric systems, Proceedings of the 41st Allerton Conference on Communication, Control, and Computing, 2003.
• S. Prajna, A. Papachristodoulou, P.A. Parrilo, Introducing SOSTOOLS: a general purpose sum of squares programming solver, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, USA, 2002.
• P.A. Parrilo, A. Doherty, F. Spedalieri, Entanglement witnesses and semidefinite programming, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, USA, 2002.
• P.A. Parrilo, Outer approximation algorithms for KYP-based LMIs, Proceedings of the American Control Conference, Arlington, USA, 2001. DOI
  
• A. Varga, P.A. Parrilo, Fast algorithms for solving $\mathcal{H}_\infty$ norm minimization problems, Proceedings of the 40st IEEE Conference on Decision and Control, Orlando, USA, 2001.
• P.A. Parrilo, Higher Order Semidefinite Relaxations for Quadratic Programming, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000.
• P.A. Parrilo, Semidefinite Programming based Tests for Matrix Copositivity, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000. DOI
  
• A. Rantzer, P.A. Parrilo, On Convexity in Stabilization of Nonlinear Systems, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000.
• P.A. Parrilo, On a Decomposition of Multivariable Forms via LMI Methods, Proceedings of the American Control Conference, Chicago, USA, 2000. DOI
  
• P.A. Parrilo, On the Numerical Solution of LMIs derived from the KYP Lemma, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, USA, 1999. DOI
  
• M. Sznaier, P.A. Parrilo, On the Gap between $\mu$ and its Upper Bound for Systems with Repeated Uncertainty Blocks, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, USA, 1999. DOI
  
• M. Sznaier, T. Amishima, J. Tierno, P.A. Parrilo, A Convex Approach for Robust $\mathcal{H}_2$ Performance Analysis, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, USA, 1999.
• P.A. Parrilo, S. Lall, F. Paganini, G. C. Verghese, B. C. Lesieutre, J. E. Marsden, Model Reduction for Analysis of Cascading Failures in Power Systems, Proceedings of the American Control Conference, San Diego, USA, 1999.
• X. Zhu, S. Khatri, P.A. Parrilo, $\mu$ with Linear Cuts: Upper Bound Computation, Proceedings of the American Control Conference, San Diego, USA, 1999.
• S. Khatri, P.A. Parrilo, Guaranteed Bounds for Probabilistic $\mu$, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, USA, 1998.
• S. Khatri, P.A. Parrilo, Spherical $\mu$, Proceedings of the American Control Conference, Philadelphia, USA, 1998. DOI
  
• P.A. Parrilo, S. Khatri, Closed Form Solutions for a Class of LMIs, Proceedings of the American Control Conference, Philadelphia, USA, 1998.
• P.A. Parrilo, R.S. Sánchez Peña, C.G. Galarza, Tuned $\ell_1$ Identification from Impulse Response Data: Application to a Fluid Dynamics Problem, Proceedings American Control Conference}, Baltimore, USA, 1994. DOI