-
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.
-
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
-
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
-
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
Last-modified: Mon Apr 10 18:20:11 EDT 2006