Preprints

Polynomial stochastic games via sum of squares optimization
P. Shah and P.A. Parrilo
http://arxiv.org/abs/0806.2469
Constrained Consensus
A. Nedic, A. Ozdaglar and P.A. Parrilo
http://arxiv.org/abs/0802.3922
Fastest mixing Markov chain on graphs with symmetries
S. Boyd, P. Diaconis, P.A. Parrilo and L. Xiao
http://arxiv.org/abs/0709.0955
Separable and Low-Rank Continuous Games
N. Stein, A. Ozdaglar and P.A. Parrilo
International Journal of Game Theory, to appear.
http://arxiv.org/abs/0707.3462
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
B. Recht, M. Fazel and P.A. Parrilo
http://arxiv.org/abs/0706.4138
Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming
E. M. Aylward, P. A. Parrilo, J.-J. E. Slotine
Automatica, to appear. DOI
http://arxiv.org/abs/math.OC/0603313
An explicit construction of distinguished representations of polynomials nonnegative over finite sets
P.A. Parrilo,
IfA Technical Report AUT02-02, March 2002.

Book chapters

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

On the asymptotic minimum number of monochromatic 3-term arithmetic progressions
P. A. Parrilo and 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
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

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.
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