Pablo A. Parrilo

Orcid: 0000-0003-1132-8477

Affiliations:
  • Dept. of Electrical Engineering and Computer Science, MIT, USA


According to our database1, Pablo A. Parrilo authored at least 162 papers between 1996 and 2024.

Collaborative distances:

Awards

IEEE Fellow

IEEE Fellow 2016, "For contributions to semidefinite and sum-of-squares optimization".

Timeline

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Bibliography

2024
Shortest Paths in Graphs of Convex Sets.
SIAM J. Optim., March, 2024

Towards Tight Convex Relaxations for Contact-Rich Manipulation.
CoRR, 2024

2023
Low-Rank Univariate Sum of Squares Has No Spurious Local Minima.
SIAM J. Optim., September, 2023

Kernel Approximation on Algebraic Varieties.
SIAM J. Appl. Algebra Geom., March, 2023

On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones.
Math. Program., March, 2023

Near-linear convergence of the Random Osborne algorithm for Matrix Balancing.
Math. Program., March, 2023

Acceleration by Stepsize Hedging I: Multi-Step Descent and the Silver Stepsize Schedule.
CoRR, 2023

2022
Approximating Min-Mean-Cycle for Low-Diameter Graphs in Near-Optimal Time and Memory.
SIAM J. Optim., September, 2022

Lifting for Simplicity: Concise Descriptions of Convex Sets.
SIAM Rev., 2022

Maximizing products of linear forms, and the permanent of positive semidefinite matrices.
Math. Program., 2022

Convergence rate of block-coordinate maximization Burer-Monteiro method for solving large SDPs.
Math. Program., 2022

On the local stability of semidefinite relaxations.
Math. Program., 2022

Solving Least Squares Problems on Partially Ordered Sets.
Proceedings of the 61st IEEE Conference on Decision and Control, 2022

2021
Why random reshuffling beats stochastic gradient descent.
Math. Program., 2021

Semidefinite Relaxations of Products of Nonnegative Forms on the Sphere.
CoRR, 2021

Preface.
Proceedings of the 3rd Annual Conference on Learning for Dynamics and Control, 2021

2020
Certifying Unstability of Switched Systems Using Sum of Squares Programming.
SIAM J. Control. Optim., 2020

Lyapunov Exponent of Rank-One Matrices: Ergodic Formula and Inapproximability of the Optimal Distribution.
SIAM J. Control. Optim., 2020

Dimension reduction for semidefinite programs via Jordan algebras.
Math. Program., 2020

Random Osborne: a simple, practical algorithm for Matrix Balancing in near-linear time.
CoRR, 2020

2019
An Entropy-Based Bound for the Computational Complexity of a Switched System.
IEEE Trans. Autom. Control., 2019

Convergence Rate of Incremental Gradient and Incremental Newton Methods.
SIAM J. Optim., 2019

Semidefinite Approximations of the Matrix Logarithm.
Found. Comput. Math., 2019

2018
Pricing Equilibria and Graphical Valuations.
ACM Trans. Economics and Comput., 2018

Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone.
Math. Program., 2018

2017
Some Recent Directions in Algebraic Methods for Optimization and Lyapunov Analysis.
Proceedings of the Geometric and Numerical Foundations of Movements, 2017

Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs.
IEEE Trans. Autom. Control., 2017

A Characterization of Lyapunov Inequalities for Stability of Switched Systems.
IEEE Trans. Autom. Control., 2017

Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems.
IEEE Trans. Autom. Control., 2017

On the Convergence Rate of Incremental Aggregated Gradient Algorithms.
SIAM J. Optim., 2017

Sampling Algebraic Varieties for Sum of Squares Programs.
SIAM J. Optim., 2017

Chordal Networks of Polynomial Ideals.
SIAM J. Appl. Algebra Geom., 2017

Equivariant Semidefinite Lifts of Regular Polygons.
Math. Oper. Res., 2017

When Cyclic Coordinate Descent Outperforms Randomized Coordinate Descent.
Proceedings of the Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 2017

2016
Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach.
SIAM J. Discret. Math., 2016

Sparse sums of squares on finite abelian groups and improved semidefinite lifts.
Math. Program., 2016

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank.
Math. Program., 2016

Generating Unstable Trajectories for Switched Systems via Dual Sum-Of-Squares Techniques.
Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, 2016

2015
Weighted ℓ<sub>1</sub>-Minimization for Generalized Non-Uniform Sparse Model.
IEEE Trans. Inf. Theory, 2015

Semidefinite Descriptions of the Convex Hull of Rotation Matrices.
SIAM J. Optim., 2015

Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies.
SIAM J. Optim., 2015

Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones.
Math. Program., 2015

The 2013 Newton Institute Programme on polynomial optimization.
Math. Program., 2015

A globally convergent incremental Newton method.
Math. Program., 2015

Approximate cone factorizations and lifts of polytopes.
Math. Program., 2015

Lower bounds on nonnegative rank via nonnegative nuclear norms.
Math. Program., 2015

Positive semidefinite rank.
Math. Program., 2015

Iterative Auction Design for Tree Valuations.
Oper. Res., 2015

An efficient tree decomposition method for permanents and mixed discriminants.
CoRR, 2015

Finding sparse, equivalent SDPs using minimal coordinate projections.
Proceedings of the 54th IEEE Conference on Decision and Control, 2015

Sparse sum-of-squares certificates on finite abelian groups.
Proceedings of the 54th IEEE Conference on Decision and Control, 2015

2014
Joint Spectral Radius and Path-Complete Graph Lyapunov Functions.
SIAM J. Control. Optim., 2014

Semidefinite relaxations for optimization problems over rotation matrices.
Proceedings of the 53rd IEEE Conference on Decision and Control, 2014

Basis selection for SOS programs via facial reduction and polyhedral approximations.
Proceedings of the 53rd IEEE Conference on Decision and Control, 2014

Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization.
Proceedings of the 53rd IEEE Conference on Decision and Control, 2014

Optimal output feedback architecture for triangular LQG problems.
Proceedings of the American Control Conference, 2014

2013
Near-Potential Games: Geometry and Dynamics.
ACM Trans. Economics and Comput., 2013

<i>H</i><sub>2</sub> -Optimal Decentralized Control Over Posets: A State-Space Solution for State-Feedback.
IEEE Trans. Autom. Control., 2013

A Complete Characterization of the Gap between Convexity and SOS-Convexity.
SIAM J. Optim., 2013

NP-hardness of deciding convexity of quartic polynomials and related problems.
Math. Program., 2013

Lifts of Convex Sets and Cone Factorizations.
Math. Oper. Res., 2013

Dynamics in near-potential games.
Games Econ. Behav., 2013

Analysis of weighted ℓ<sub>1</sub>-minimization for model based compressed sensing
CoRR, 2013

Exchangeable Equilibria, Part I: Symmetric Bimatrix Games.
CoRR, 2013

SOSTOOLS Version 3.00 Sum of Squares Optimization Toolbox for MATLAB.
CoRR, 2013

Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity.
CoRR, 2013

Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions.
CoRR, 2013

Convex algebraic geometry and semidefinite optimization.
Proceedings of the International Symposium on Symbolic and Algebraic Computation, 2013

Diagonal and low-rank decompositions and fitting ellipsoids to random points.
Proceedings of the 52nd IEEE Conference on Decision and Control, 2013

2012
Convex Graph Invariants.
SIAM Rev., 2012

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting.
SIAM J. Matrix Anal. Appl., 2012

A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs.
Math. Program., 2012

A convex polynomial that is not sos-convex.
Math. Program., 2012

The Convex Geometry of Linear Inverse Problems.
Found. Comput. Math., 2012

Rejoinder: Latent variable graphical model selection via convex optimization
CoRR, 2012

Reconstructing the unknown, balancing structure and uncertainty: technical perspective.
Commun. ACM, 2012

When Is a Set of LMIs a Sufficient Condition for Stability?
Proceedings of the 7th IFAC Symposium on Robust Control Design, 2012

Selecting a monomial basis for sums of squares programming over a quotient ring.
Proceedings of the 51th IEEE Conference on Decision and Control, 2012

Joint spectral radius of rank one matrices and the maximum cycle mean problem.
Proceedings of the 51th IEEE Conference on Decision and Control, 2012

2011
A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization.
IEEE Trans. Autom. Control., 2011

Rank-Sparsity Incoherence for Matrix Decomposition.
SIAM J. Optim., 2011

Flows and Decompositions of Games: Harmonic and Potential Games.
Math. Oper. Res., 2011

Structure of extreme correlated equilibria: a zero-sum example and its implications.
Int. J. Game Theory, 2011

Correlated equilibria in continuous games: Characterization and computation.
Games Econ. Behav., 2011

H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback
CoRR, 2011

Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs.
Proceedings of the 14th ACM International Conference on Hybrid Systems: Computation and Control, 2011

An optimal controller architecture for poset-causal systems.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

Tree-structured statistical modeling via convex optimization.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

Learning in near-potential games.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

Converse results on existence of sum of squares Lyapunov functions.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

On higher order derivatives of Lyapunov functions.
Proceedings of the American Control Conference, 2011

2010
Constrained Consensus and Optimization in Multi-Agent Networks.
IEEE Trans. Autom. Control., 2010

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization.
SIAM Rev., 2010

Theta Bodies for Polynomial Ideals.
SIAM J. Optim., 2010

Optimality of Affine Policies in Multistage Robust Optimization.
Math. Oper. Res., 2010

Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods.
J. Comput. Phys., 2010

A new proof of Nash's Theorem via exchangeable equilibria
CoRR, 2010

Structure of Extreme Correlated Equilibria
CoRR, 2010

Near-Optimal Power Control in Wireless Networks: A Potential Game Approach.
Proceedings of the INFOCOM 2010. 29th IEEE International Conference on Computer Communications, 2010

ℋ2-optimal decentralized control over posets: A state space solution for state-feedback.
Proceedings of the 49th IEEE Conference on Decision and Control, 2010

A projection framework for near-potential games.
Proceedings of the 49th IEEE Conference on Decision and Control, 2010

On the equivalence of algebraic conditions for convexity and quasiconvexity of polynomials.
Proceedings of the 49th IEEE Conference on Decision and Control, 2010

The Convex algebraic geometry of linear inverse problems.
Proceedings of the 48th Annual Allerton Conference on Communication, 2010

Latent variable graphical model selection via convex optimization.
Proceedings of the 48th Annual Allerton Conference on Communication, 2010

Dynamics in near-potential games.
Proceedings of the 48th Annual Allerton Conference on Communication, 2010

2009
Fastest Mixing Markov Chain on Graphs with Symmetries.
SIAM J. Optim., 2009

Competitive scheduling in wireless collision channels with correlated channel state.
Proceedings of the 1st International Conference on Game Theory for Networks, 2009

A poset framework to model decentralized control problems.
Proceedings of the 48th IEEE Conference on Decision and Control, 2009

Optimality of affine policies in multi-stage robust optimization.
Proceedings of the 48th IEEE Conference on Decision and Control, 2009

A positive definite polynomial Hessian that does not factor.
Proceedings of the 48th IEEE Conference on Decision and Control, 2009

Sparse and low-rank matrix decompositions.
Proceedings of the 47th Annual Allerton Conference on Communication, 2009

2008
Computing sum of squares decompositions with rational coefficients.
Theor. Comput. Sci., 2008

On the asymptotic minimum number of monochromatic 3-term arithmetic progressions.
J. Comb. Theory, Ser. A, 2008

Separable and low-rank continuous games.
Int. J. Game Theory, 2008

Structured semidefinite programs for the control of symmetric systems.
Autom., 2008

Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming.
Autom., 2008

Computing correlated equilibria of polynomial games via adaptive discretization.
Proceedings of the 47th IEEE Conference on Decision and Control, 2008

A Partial order approach to decentralized control.
Proceedings of the 47th IEEE Conference on Decision and Control, 2008

Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems.
Proceedings of the 47th IEEE Conference on Decision and Control, 2008

A partial order approach to decentralized control of spatially invariant systems.
Proceedings of the 46th Annual Allerton Conference on Communication, 2008

Compressed sensing and robust recovery of low rank matrices.
Proceedings of the 42nd Asilomar Conference on Signals, Systems and Computers, 2008

2007
Efficient classification of complete parameter regions based on semidefinite programming.
BMC Bioinform., 2007

A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients.
Proceedings of the Symbolic-Numeric Computation, 2007

Approximation of the Joint Spectral Radius of a Set of Matrices Using Sum of Squares.
Proceedings of the Hybrid Systems: Computation and Control, 10th International Workshop, 2007

Solving commutative relaxations of word problems.
Proceedings of the 46th IEEE Conference on Decision and Control, 2007

Characterization and computation of correlated equilibria in infinite games.
Proceedings of the 46th IEEE Conference on Decision and Control, 2007

Polynomial stochastic games via sum of squares optimization.
Proceedings of the 46th IEEE Conference on Decision and Control, 2007

A theorem of the alternative for SOS Lyapunov functions.
Proceedings of the 46th IEEE Conference on Decision and Control, 2007

Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma.
Proceedings of the 46th IEEE Conference on Decision and Control, 2007

2006
A PTAS for the minimization of polynomials of fixed degree over the simplex.
Theor. Comput. Sci., 2006

Polynomial games and sum of squares optimization.
Proceedings of the 45th IEEE Conference on Decision and Control, 2006

Algorithmic search for contraction metrics via SOS programming.
Proceedings of the American Control Conference, 2006

2005
Symmetry Analysis of Reversible Markov Chains.
Internet Math., 2005

SOS Methods for Semi-algebraic Games and Optimization.
Proceedings of the Hybrid Systems: Computation and Control, 8th International Workshop, 2005

Nonlinear parametric optimization using cylindrical algebraic decomposition.
Proceedings of the 44th IEEE IEEE Conference on Decision and Control and 8th European Control Conference Control, 2005

2004
Nonlinear control synthesis by convex optimization.
IEEE Trans. Autom. Control., 2004

An Inequality for Circle Packings Proved by Semidefinite Programming.
Discret. Comput. Geom., 2004

Sums of squares of polynomials and their applications.
Proceedings of the Symbolic and Algebraic Computation, 2004

From coefficients to samples: a new approach to SOS optimization.
Proceedings of the 43rd IEEE Conference on Decision and Control, 2004

New developments in sum of squares optimization and SOSTOOLS.
Proceedings of the 2004 American Control Conference, 2004

Nonlinear stability via sum of squares programming.
Proceedings of the 2004 American Control Conference, 2004

2003
Semidefinite programming relaxations for semialgebraic problems.
Math. Program., 2003

Semidefinite Programming Relaxations and Algebraic Optimization in Control.
Eur. J. Control, 2003

Stability & feasibility of constrained receding horizon control.
Proceedings of the 7th European Control Conference, 2003

Exploiting structure in sum of squares programs.
Proceedings of the 42nd IEEE Conference on Decision and Control, 2003

Robust Receding Horizon Control - analysis &amp; synthesis.
Proceedings of the 42nd IEEE Conference on Decision and Control, 2003

2002
A convex approach to robust H<sub>2</sub> performance analysis.
Autom., 2002

Introducing SOSTOOLS: a general purpose sum of squares programming solver.
Proceedings of the 41st IEEE Conference on Decision and Control, 2002

Entanglement witnesses and semidefinite programming.
Proceedings of the 41st IEEE Conference on Decision and Control, 2002

2001
Robust identification with mixed parametric/nonparametric models and time/frequency-domain experiments: theory and an application.
IEEE Trans. Control. Syst. Technol., 2001

Minimizing Polynomial Functions.
Proceedings of the Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2001

Fast algorithms for solving H<sub>∞</sub>-norm minimization problems.
Proceedings of the 40th IEEE Conference on Decision and Control, 2001

Outer approximation algorithms for KYP-based LMIs.
Proceedings of the American Control Conference, 2001

2000
On cone-invariant linear matrix inequalities.
IEEE Trans. Autom. Control., 2000

On convexity in stabilization of nonlinear systems.
Proceedings of the 39th IEEE Conference on Decision and Control, 2000

Semidefinite programming based tests for matrix copositivity.
Proceedings of the 39th IEEE Conference on Decision and Control, 2000

Higher order semi-definite relaxations for quadratic programming.
Proceedings of the 39th IEEE Conference on Decision and Control, 2000

On a decomposition of multivariable forms via LMI methods.
Proceedings of the American Control Conference, 2000

1999
A parametric extension of mixed time/frequency robust identification.
IEEE Trans. Autom. Control., 1999

1998
Mixed Time/Frequency-Domain Based Robust Identification.
Autom., 1998

1996
l<sub>1</sub> identification applied to a fluid dynamics problem.
IEEE Trans. Control. Syst. Technol., 1996


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