Pablo Parrilo
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Control Theory
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Mathematics Engineering
Pablo Parrilo's Degrees
- PhD Control and Dynamical Systems California Institute of Technology
- Masters Electrical Engineering California Institute of Technology
Why Is Pablo Parrilo Influential?
(Suggest an Edit or Addition)According to Wikipedia, Pablo A. Parrilo from MIT was named Fellow of the Institute of Electrical and Electronics Engineers in 2016 for contributions to semidefinite and sum-of-squares optimization. He was named a SIAM Fellow in 2018.
Pablo Parrilo's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization (2007) (3560)
- Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization (2000) (2186)
- Constrained Consensus and Optimization in Multi-Agent Networks (2008) (1689)
- Semidefinite programming relaxations for semialgebraic problems (2003) (1622)
- The Convex Geometry of Linear Inverse Problems (2010) (1260)
- Rank-Sparsity Incoherence for Matrix Decomposition (2009) (1075)
- SOSTOOLS: Sum of squares optimization toolbox for MATLAB (2002) (716)
- Semidefinite Optimization and Convex Algebraic Geometry (2012) (594)
- Introducing SOSTOOLS: a general purpose sum of squares programming solver (2002) (556)
- Latent variable graphical model selection via convex optimization (2010) (485)
- Minimizing Polynomial Functions (2001) (373)
- Symmetry groups, semidefinite programs, and sums of squares (2002) (364)
- Complete family of separability criteria (2003) (316)
- Nonlinear control synthesis by convex optimization (2004) (291)
- Distinguishing separable and entangled states. (2001) (277)
- Optimality of Affine Policies in Multistage Robust Optimization (2009) (224)
- The lax conjecture is true (2003) (188)
- Lifts of Convex Sets and Cone Factorizations (2011) (180)
- Flows and Decompositions of Games: Harmonic and Potential Games (2010) (170)
- Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming (2006) (160)
- SOSTOOLS Version 3.00 Sum of Squares Optimization Toolbox for MATLAB (2013) (159)
- Sparse and low-rank matrix decompositions (2009) (157)
- ℋ2-optimal decentralized control over posets: A state space solution for state-feedback (2010) (151)
- Semidefinite Programming Relaxations and Algebraic Optimization in Control (2003) (150)
- Approximation of the joint spectral radius using sum of squares (2007) (144)
- On the Convergence Rate of Incremental Aggregated Gradient Algorithms (2015) (141)
- Theta Bodies for Polynomial Ideals (2008) (141)
- $ {\cal H}_{2}$-Optimal Decentralized Control Over Posets: A State-Space Solution for State-Feedback (2010) (131)
- A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization (2011) (130)
- Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems (2008) (121)
- Computing sum of squares decompositions with rational coefficients (2008) (119)
- Fastest Mixing Markov Chain on Graphs with Symmetries (2007) (118)
- Compressed sensing and robust recovery of low rank matrices (2008) (118)
- SOSTOOLS and its control applications (2005) (116)
- Why random reshuffling beats stochastic gradient descent (2015) (115)
- NP-hardness of deciding convexity of quartic polynomials and related problems (2010) (115)
- A PTAS for the minimization of polynomials of fixed degree over the simplex (2006) (110)
- Positive semidefinite rank (2014) (97)
- Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs (2014) (94)
- Optimality of affine policies in multi-stage robust optimization (2009) (94)
- Joint Spectral Radius and Path-Complete Graph Lyapunov Functions (2011) (91)
- Parametric optimization and optimal control using algebraic geometry methods (2006) (88)
- A convex polynomial that is not sos-convex (2009) (78)
- Detecting multipartite entanglement (2004) (76)
- Dynamics in near-potential games (2010) (76)
- Near-Optimal Power Control in Wireless Networks: A Potential Game Approach (2010) (75)
- Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone (2014) (75)
- Model reduction for analysis of cascading failures in power systems (1999) (74)
- A Complete Characterization of the Gap between Convexity and SOS-Convexity (2011) (74)
- A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function (2011) (72)
- Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting (2012) (71)
- Efficient classification of complete parameter regions based on semidefinite programming (2007) (70)
- New developments in sum of squares optimization and SOSTOOLS (2004) (69)
- Semidefinite Approximations of the Matrix Logarithm (2017) (67)
- Symmetry Analysis of Reversible Markov Chains (2005) (64)
- Semidefinite Descriptions of the Convex Hull of Rotation Matrices (2014) (59)
- The Convex algebraic geometry of linear inverse problems (2010) (59)
- Polynomial games and sum of squares optimization (2006) (59)
- Semidefinite Representation of the k-Ellipse (2007) (58)
- Nonlinear parametric optimization using cylindrical algebraic decomposition (2005) (58)
- From coefficients to samples: a new approach to SOS optimization (2004) (58)
- Separable and low-rank continuous games (2006) (56)
- Robust Receding Horizon Control - analysis & synthesis (2003) (56)
- Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods (2009) (50)
- A globally convergent incremental Newton method (2014) (49)
- An explicit construction of distinguished representations of polynomials nonnegative over finite sets (2002) (46)
- A Partial order approach to decentralized control (2008) (46)
- Exploiting Algebraic Structure in Sum of Squares Programs (2005) (44)
- Mixed time/frequency-domain based robust identification (1998) (43)
- Design of photonic crystals with multiple and combined band gaps. (2011) (42)
- Quantum algorithms for the ordered search problem via semidefinite programming (2006) (42)
- On the equivalence of algebraic approaches to the minimization of forms on the simplex (2005) (41)
- Initialization of Physical Parameter Estimates (2003) (40)
- Analysis of the joint spectral radius via lyapunov functions on path-complete graphs (2011) (39)
- Converse results on existence of sum of squares Lyapunov functions (2011) (39)
- Structured semidefinite programs for the control of symmetric systems (2008) (38)
- On convexity in stabilization of nonlinear systems (2000) (36)
- SOSTOOLS: control applications and new developments (2004) (34)
- Chapter 3: Polynomial Optimization, Sums of Squares, and Applications (2012) (34)
- Basis selection for SOS programs via facial reduction and polyhedral approximations (2014) (34)
- On the local stability of semidefinite relaxations (2017) (34)
- On cone-invariant linear matrix inequalities (2000) (32)
- A Characterization of Lyapunov Inequalities for Stability of Switched Systems (2016) (31)
- Robustness and the Internet : Theoretical Foundations (2002) (30)
- On the numerical solution of LMIs derived from the KYP lemma (1999) (30)
- Complete family of separability criteria (20 pages) (2004) (30)
- Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma (2007) (30)
- Near-Potential Games: Geometry and Dynamics (2013) (30)
- Exploiting structure in sum of squares programs (2003) (29)
- On higher order derivatives of Lyapunov functions (2011) (29)
- Correlated equilibria in continuous games: Characterization and computation (2008) (28)
- Robust identification with mixed parametric/nonparametric models and time/frequency-domain experiments: theory and an application (1999) (28)
- A parametric extension of mixed time/frequency robust identification (1999) (28)
- Iterative Auction Design for Tree Valuations (2015) (27)
- On a decomposition of multivariable forms via LMI methods (2000) (27)
- Convergence Rate of Incremental Gradient and Incremental Newton Methods (2015) (27)
- Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank (2014) (26)
- Optimal output feedback architecture for triangular LQG problems (2014) (26)
- Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones (2012) (26)
- Sparse sums of squares on finite abelian groups and improved semidefinite lifts (2016) (26)
- When Cyclic Coordinate Descent Outperforms Randomized Coordinate Descent (2017) (26)
- Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization (2014) (25)
- Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach (2014) (25)
- Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies (2013) (25)
- On the asymptotic minimum number of monochromatic 3-term arithmetic progressions (2006) (24)
- An optimal controller architecture for poset-causal systems (2011) (24)
- A convex approach to robust H2 performance analysis (2002) (24)
- An efficient tree decomposition method for permanents and mixed discriminants (2015) (23)
- Sparse sum-of-squares certificates on finite abelian groups (2015) (23)
- Convergence Rate of Incremental Gradient and Newton Methods (2015) (23)
- A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs (2009) (22)
- Mixed time/frequency-domain based robust identification (1996) (21)
- Convergence rate of block-coordinate maximization Burer–Monteiro method for solving large SDPs (2018) (21)
- An Inequality for Circle Packings Proved by Semidefinite Programming (2004) (20)
- Fast algorithms for solving H/sub /spl infin//-norm minimization problems (2001) (20)
- Convex graph invariants (2010) (19)
- Sampling Algebraic Varieties for Sum of Squares Programs (2015) (19)
- A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients (2007) (18)
- NSF Workshop in Cyber-Physical Systems (2006) (18)
- Sum of Squares Programs and Polynomial Inequalities (2004) (18)
- Semidefinite relaxations for optimization problems over rotation matrices (2014) (18)
- Competitive scheduling in wireless collision channels with correlated channel state (2009) (17)
- Computation with Polynomial Equations and Inequalities Arising in Combinatorial Optimization (2009) (16)
- Joint spectral radius of rank one matrices and the maximum cycle mean problem (2012) (16)
- A projection framework for near-potential games (2010) (16)
- Generating Unstable Trajectories for Switched Systems via Dual Sum-Of-Squares Techniques (2016) (16)
- Sum of Squares Optimization Toolbox for MATLAB User ’ s guide Version 2 . 00 June 1 , 2004 (2004) (15)
- Lower bounds on nonnegative rank via nonnegative nuclear norms (2012) (15)
- Semidefinite programming based tests for matrix copositivity (2000) (15)
- Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions (2013) (15)
- Pricing Equilibria and Graphical Valuations (2015) (13)
- A parametric extension of mixed time/frequency robust identification (1997) (13)
- Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems (2017) (13)
- Dimension reduction for semidefinite programs via Jordan algebras (2016) (13)
- Approximation of the Joint Spectral Radius of a Set of Matrices Using Sum of Squares (2007) (13)
- Selecting a monomial basis for sums of squares programming over a quotient ring (2012) (12)
- Chordal networks of polynomial ideals (2016) (12)
- Algorithmic search for contraction metrics via SOS programming (2006) (12)
- Convex Quantifier Elimination for Semidefinite Programming (2003) (12)
- Outer approximation algorithms for KYP-based LMIs (2001) (12)
- Approximate cone factorizations and lifts of polytopes (2013) (11)
- Equivariant Semidefinite Lifts of Regular Polygons (2014) (11)
- Shortest Paths in Graphs of Convex Sets (2021) (10)
- A poset framework to model decentralized control problems (2009) (10)
- When Is a Set of LMIs a Sufficient Condition for Stability? (2012) (10)
- Polynomial stochastic games via sum of squares optimization (2007) (10)
- Convex algebraic geometry and semidefinite optimization (2013) (10)
- Guaranteed bounds for probabilistic /spl mu/ (1998) (9)
- Characterization and computation of correlated equilibria in infinite games (2007) (9)
- A positive definite polynomial Hessian that does not factor (2009) (9)
- Finding sparse, equivalent SDPs using minimal coordinate projections (2015) (9)
- Sums of squares in Macaulay2 (2018) (9)
- Learning in near-potential games (2011) (9)
- Stability & feasibility of constrained receding horizon control (2003) (9)
- On the equivalence of algebraic conditions for convexity and quasiconvexity of polynomials (2010) (9)
- On the gap between /spl mu/ and its upper bound for systems with repeated uncertainty blocks (1999) (8)
- New lower bounds on nonnegative rank using conic programming (2012) (8)
- Robust Identification: An approach to select the class of candidate models (2001) (8)
- A Hierarchy of Near-Optimal Policies for (2011) (7)
- Lifting for Simplicity: Concise Descriptions of Convex Sets (2020) (7)
- On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones (2021) (7)
- Convex Solution to a Joint Attitude and Spin-Rate Estimation Problem (2014) (7)
- Random Osborne: a simple, practical algorithm for Matrix Balancing in near-linear time (2020) (7)
- Weighted $\ell _{1}$ -Minimization for Generalized Non-Uniform Sparse Model (2013) (7)
- Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity (2013) (6)
- A partial order approach to decentralized control of spatially invariant systems (2008) (6)
- Sums of squares of polynomials and their applications (2004) (6)
- Diagonal and low-rank decompositions and fitting ellipsoids to random points (2013) (6)
- Sum of Squares and Polynomial Convexity (2009) (6)
- A theorem of the alternative for SOS Lyapunov functions (2007) (6)
- REJOINDER: LATENT VARIABLE GRAPHICAL MODEL SELECTION VIA CONVEX OPTIMIZATION (2017) (5)
- Spherical /spl mu/ (1998) (5)
- Sum of Squares Optimization Toolbox for MATLAB User ’ s guide Version 4 . 00 14 th September 2021 (2021) (5)
- /spl mu/ with linear cuts: upper bound computation (1999) (5)
- SOS Methods for Semi-algebraic Games and Optimization (2005) (5)
- Exchangeable equilibria contradict exactness of the Papadimitriou-Roughgarden algorithm (2010) (5)
- Erratum: Design of photonic crystals with multiple and combined band gaps [Phys. Rev. E83, 046703 (2011)] (2012) (5)
- Approximating Min-Mean-Cycle for low-diameter graphs in near-optimal time and memory (2020) (5)
- Iterative Auction Design for Graphical Valuations Part I : Tree Valuations ∗ (2013) (5)
- An Entropy-Based Bound for the Computational Complexity of a Switched System (2019) (4)
- A geometric inequality for circle packings (2002) (4)
- How to Flatten a Soccer Ball (2016) (4)
- Maximizing products of linear forms, and the permanent of positive semidefinite matrices (2020) (4)
- Theory and Algorithms of Linear Matrix Inequalities Questions and Discussions of the Literature (4)
- Near-linear convergence of the Random Osborne algorithm for Matrix Balancing (2020) (4)
- Certifying Unstability of Switched Systems Using Sum of Squares Programming (2017) (4)
- Entanglement witnesses and semidefinite programming (2002) (4)
- Mit 6.972 Algebraic Techniques and Semidefinite Optimization (2006) (4)
- Iterative Auction Design for Graphical Valuations Part II : General Graphs ∗ (2014) (4)
- A Hierarchy of Suboptimal Policies for the Multi-period , Multi-echelon , Robust Inventory Problem (2009) (4)
- Nonlinear stability via sum of squares programming (2004) (3)
- Higher order semi-definite relaxations for quadratic programming (2000) (3)
- A new proof of Nash's Theorem via exchangeable equilibria (2010) (3)
- Structure of Extreme Correlated Equilibria (2010) (3)
- A new semidefinite programming relaxation for cycles in binary matroids and cuts in graphs (2012) (3)
- Minimum-strain symmetrization of Bravais lattices (2019) (3)
- Fast Algorithms for Solving H-infinity-Norm Minimization Problems (2001) (3)
- Some Recent Directions in Algebraic Methods for Optimization and Lyapunov Analysis (2017) (3)
- Lecture 9 (2018) (3)
- Computing correlated equilibria of polynomial games via adaptive discretization (2008) (3)
- Tree-structured statistical modeling via convex optimization (2011) (3)
- Analysis of weighted ℓ1-minimization for model based compressed sensing (2013) (2)
- Exchangeable Equilibria, Part I: Symmetric Bimatrix Games (2013) (2)
- Lyapunov Exponent of Rank-One Matrices: Ergodic Formula and Inapproximability of the Optimal Distribution (2019) (2)
- Tuned l/sub 1/ identification from impulse response data: application to a fluid dynamics problem (1994) (2)
- Structure of extreme correlated equilibria: a zero-sum example and its implications (2010) (2)
- Closed form solutions for a class of LMIs (1998) (2)
- Kernel approximation on algebraic varieties (2021) (1)
- Chapter 2: Semidefinite Optimization (2012) (1)
- Acm270 Algebraic Techniques and Semidefinite Optimization (2007) (1)
- A partial proof of Nash's Theorem via exchangeable equilibria (2010) (1)
- Low-Rank Univariate Sum of Squares Has No Spurious Local Minima (2022) (1)
- Polynomial Ideals (2006) (1)
- Dynamics in Near-Potential Games (Extended Abstract) (2010) (1)
- Piecewise polynomial Lyapunov functions with guaranteed accuracy (2010) (0)
- Convergent Adaptive Discretization Methods for Computing Correlated Equilibria of Polynomial Games (2008) (0)
- Weighted (cid:96) 1 -minimization for generalized non-uniform sparse model (2014) (0)
- Solving commutative relaxations of word problems (2007) (0)
- Reconstructing the unknown, balancing structure and uncertainty (2012) (0)
- An error in the proof of Nash's Theorem via exchangeable equilibria (2010) (0)
- Proving and Solving Semi-definite Programming over Reals (Computer Algebra : Algorithms, Implementations and Applications) (2003) (0)
- L1 Identification Applied to a Fluid Dynamics Problem (1996) (0)
- Approximate cone factorizations and lifts of polytopes (2014) (0)
- Specification, Design and Verification of Distributed Embedded Systems (2010) (0)
- Sparse sums of squares on finite abelian groups and improved semidefinite lifts (2016) (0)
- Semidefinite Approximations of the Matrix Logarithm (2018) (0)
- LIDS Technical Report # 2779 1 Constrained Consensus ∗ (2008) (0)
- Joint spectral radius, path-complete graphs, and semidefinite programming (2012) (0)
- The 2013 Newton Institute Programme on polynomial optimization (2015) (0)
- A convex approach to robust H/sub 2/ performance analysis (1999) (0)
- Maximizing products of linear forms, and the permanent of positive semidefinite matrices (2021) (0)
- On the Convergence of Block-Coordinate Maximization for Burer-Monteiro Method (2018) (0)
- Recovering a measure from its moments (2006) (0)
- Semidefinite Relaxations of Products of Nonnegative Forms on the Sphere (2021) (0)
- Sparse sum-of-squares certicates on (2015) (0)
- Sum of squares programs: what are they good for, and how to solve them (2004) (0)
- Inclusion of Frequency Domain Behaviors (2002) (0)
- Chapter 1: What is Convex Algebraic Geometry? (2012) (0)
- Binary Optimization (2006) (0)
- • For all x ∈ R n, x T Ax ≥ 0. (2006) (0)
- Dimension reduction for semidefinite programs via Jordan algebras (2019) (0)
- A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs (2010) (0)
- Simulation-based analysis of cascading failure for power networks (2007) (0)
- Randomization, Relaxation, and Complexity (2010) (0)
- Focused Polynomials , Random Projections and Approximation Algorithms for Polynomial Optimization over the Sphere by Chenyang Yuan (2019) (0)
- Band-Gap Optimization for Wave Propagation in Periodic Media using Semi-Definite Programming (2011) (0)
- Lyapunov Exponent of Rank One Matrices: Ergodic Formula and Inapproximability of the Optimal Distribution (2019) (0)
- Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones (2014) (0)
- Robust identification with mixed time/frequency-domain experiments: theory and an application (1997) (0)
- Monomial orderings Recall from last lecture the notion of a monomial ordering : Definition 1 (2006) (0)
- Solving Least Squares Problems on Partially Ordered Sets (2022) (0)
- Parrilo Scribe : ? ? ? 1 SDP representability (2006) (0)
- Preface: The 2013 Newton Institute programme on polynomial optimisation (2015) (0)
- A globally convergent incremental Newton method (2015) (0)
- Domain Partitioning to Bound Moments of Differential Equations Using Semidefinite Optimization (2007) (0)
- A convex polynomial that is not sos-convex (2011) (0)
- Preface (2021) (0)
- 2 Notation , Terminology , and Basics (2008) (0)
- The 2013 Newton Institute Programme on polynomial optimization (2015) (0)
- 2 7 M ay 2 00 2 A geometric inequality for circle packings (2008) (0)
- Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank (2015) (0)
- Analysis of weightedl1-minimization for model-based compressed sensing (2013) (0)
- Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone (2017) (0)
- 01 12 00 7 v 3 2 A pr 2 00 2 Distinguishing separable and entangled states (2018) (0)
- Low Rank Matrix Completion by Feng Nan (2010) (0)
- A hierarchy of policies for adaptive optimization (2011) (0)
- Fellowships, Grants, & Awards (2004) (0)
- Finding quantum algorithms via convex optimization (2007) (0)
- Positive semidefinite rank (2015) (0)
- Certificates Talk about certificates in QE (2006) (0)
- Fast algorithms for solving H∞-norm minimization problems (2001) (0)
- NP-hardness of deciding convexity of quartic polynomials and related problems (2011) (0)
- N ov 2 00 3 A complete family of separability criteria (2003) (0)
- Lower bounds on nonnegative rank via nonnegative nuclear norms (2014) (0)
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