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1

The Convex Geometry of Linear Inverse Problems

Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, Alan S. Willsky

Journal:

Foundations of Computational Mathematics

Year:

2012

Language:

english

File:

PDF, 1.42 MB

english, 2012

2

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

Recht, Benjamin, Fazel, Maryam, Parrilo, Pablo A.

Journal:

Year:

2010

Language:

english

File:

PDF, 404 KB

english, 2010

3

Complete family of separability criteria

Doherty, Andrew C., Parrilo, Pablo A., Spedalieri, Federico M.

Journal:

Physical Review A

Year:

2004

Language:

english

File:

PDF, 214 KB

english, 2004

4

Symmetry Analysis of Reversible Markov Chains

Boyd, Stephen, Diaconis, Persi, Parrilo, Pablo, Xiao, Lin

Journal:

Internet Mathematics

Year:

2005

Language:

english

File:

PDF, 566 KB

english, 2005

5

Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies

Fawzi, Hamza, Saunderson, James, Parrilo, Pablo A.

Journal:

SIAM Journal on Optimization

Year:

2015

Language:

english

File:

PDF, 739 KB

english, 2015

6

Flows and Decompositions of Games: Harmonic and Potential Games

Candogan, Ozan, Menache, Ishai, Ozdaglar, Asuman, Parrilo, Pablo A.

Journal:

Mathematics of Operations Research

Year:

2011

Language:

english

File:

PDF, 422 KB

english, 2011

7

Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming

Erin M. Aylward, Pablo A. Parrilo, Jean-Jacques E. Slotine

Journal:

Year:

2008

Language:

english

File:

PDF, 571 KB

english, 2008

8

Symmetry groups, semidefinite programs, and sums of squares

Karin Gatermann, Pablo A. Parrilo

Journal:

Journal of Pure and Applied Algebra

Year:

2004

Language:

english

File:

PDF, 395 KB

english, 2004

9

Approximation of the joint spectral radius using sum of squares

Pablo A. Parrilo, Ali Jadbabaie

Journal:

Linear Algebra and its Applications

Year:

2008

Language:

english

File:

PDF, 233 KB

english, 2008

10

A PTAS for the minimization of polynomials of fixed degree over the simplex

Etienne de Klerk, Monique Laurent, Pablo A. Parrilo

Journal:

Theoretical Computer Science

Year:

2006

Language:

english

File:

PDF, 284 KB

english, 2006

11

An Inequality for Circle Packings Proved by Semidefinite Programming

Pablo A. Parrilo, Ronen Peretz

Journal:

Discrete & Computational Geometry

Year:

2004

Language:

english

File:

PDF, 179 KB

english, 2004

12

Semidefinite programming relaxations for semialgebraic problems

Pablo A. Parrilo

Journal:

Mathematical Programming

Year:

2003

Language:

english

File:

PDF, 248 KB

english, 2003

13

Rank-Sparsity Incoherence for Matrix Decomposition

Chandrasekaran, Venkat, Sanghavi, Sujay, Parrilo, Pablo A., Willsky, Alan S.

Journal:

SIAM Journal on Optimization

Year:

2011

Language:

english

File:

PDF, 374 KB

english, 2011

14

NP-hardness of deciding convexity of quartic polynomials and related problems

Amir Ali Ahmadi, Alex Olshevsky, Pablo A. Parrilo, John N. Tsitsiklis

Journal:

Mathematical Programming

Year:

2013

Language:

english

File:

PDF, 274 KB

english, 2013

15

Distinguishing Separable and Entangled States

Doherty, A. C., Parrilo, Pablo A., Spedalieri, Federico M.

Journal:

Physical Review Letters

Year:

2002

Language:

english

File:

PDF, 93 KB

english, 2002

16

Semidefinite Optimization and Convex Algebraic Geometry || Chapter 3: Polynomial Optimization, Sums of Squares, and Applications

Blekherman, Grigoriy, Parrilo, Pablo A., Thomas, Rekha R.

Year:

2012

Language:

english

File:

PDF, 2.81 MB

english, 2012

17

$ {\cal H}_{2}$-Optimal Decentralized Control Over Posets: A State-Space Solution for State-Feedback

Shah, Parikshit, Parrilo, Pablo A.

Journal:

IEEE Transactions on Automatic Control

Year:

2013

Language:

english

File:

PDF, 2.73 MB

english, 2013

18

A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

Bertsimas, Dimitris, Iancu, Dan Andrei, Parrilo, Pablo A.

Journal:

IEEE Transactions on Automatic Control

Year:

2011

Language:

english

File:

PDF, 690 KB

english, 2011

19

Semidefinite Optimization and Convex Algebraic Geometry || Chapter 1: What is Convex Algebraic Geometry?

Blekherman, Grigoriy, Parrilo, Pablo A., Thomas, Rekha R.

Year:

2012

Language:

english

File:

PDF, 51 KB

english, 2012

20

Semidefinite Optimization and Convex Algebraic Geometry || Back Matter

Blekherman, Grigoriy, Parrilo, Pablo A., Thomas, Rekha R.

Year:

2012

Language:

english

File:

PDF, 91 KB

english, 2012

21

Semidefinite Optimization and Convex Algebraic Geometry || Chapter 2: Semidefinite Optimization

Blekherman, Grigoriy, Parrilo, Pablo A., Thomas, Rekha R.

Year:

2012

Language:

english

File:

PDF, 2.57 MB

english, 2012

22

Semidefinite Optimization and Convex Algebraic Geometry || Chapter 4: Nonnegative Polynomials and Sums of Squares

Blekherman, Grigoriy, Parrilo, Pablo A., Thomas, Rekha R.

Year:

2012

Language:

english

File:

PDF, 400 KB

english, 2012

23

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank

Fawzi, Hamza, Parrilo, Pablo A.

Journal:

Mathematical Programming

Year:

2016

Language:

english

File:

PDF, 1.10 MB

english, 2016

24

Convex Solution to a Joint Attitude and Spin-Rate Estimation Problem

Saunderson, James, Parrilo, Pablo A., Willsky, Alan S.

Journal:

Journal of Guidance Control and Dynamics

Year:

2015

Language:

english

File:

PDF, 197 KB

english, 2015

25

Positive semidefinite rank

Fawzi, Hamza, Gouveia, João, Parrilo, Pablo A., Robinson, Richard Z., Thomas, Rekha R.

Journal:

Mathematical Programming

Year:

2015

Language:

english

File:

PDF, 1018 KB

english, 2015

26

Iterative Auction Design for Tree Valuations

Candogan, Ozan, Ozdaglar, Asuman, Parrilo, Pablo A.

Journal:

Operations Research

Year:

2015

Language:

english

File:

PDF, 382 KB

english, 2015

27

Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach

Cifuentes, Diego, Parrilo, Pablo A.

Journal:

SIAM Journal on Discrete Mathematics

Year:

2016

Language:

english

File:

PDF, 1.50 MB

english, 2016

28

A Characterization of Lyapunov Inequalities for Stability of Switched Systems

Jungers, Raphael, Ahmadi, Amir Ali, Parrilo, Pablo A., Roozbehani, Mardavij

Journal:

IEEE Transactions on Automatic Control

Year:

2017

Language:

english

File:

PDF, 457 KB

english, 2017

29

Dimension reduction for semidefinite programs via Jordan algebras

Permenter, Frank, Parrilo, Pablo A.

Journal:

Mathematical Programming

Year:

2019

Language:

english

File:

PDF, 609 KB

english, 2019

30

Structured semidefinite programs for the control of symmetric systems

Randy Cogill, Sanjay Lall, Pablo A. Parrilo

Journal:

Year:

2008

Language:

english

File:

PDF, 392 KB

english, 2008

31

On the asymptotic minimum number of monochromatic 3-term arithmetic progressions

Pablo A. Parrilo, Aaron Robertson, Dan Saracino

Journal:

Journal of Combinatorial Theory, Series A

Year:

2008

Language:

english

File:

PDF, 123 KB

english, 2008

32

Structure of extreme correlated equilibria: a zero-sum example and its implications

Noah D. Stein, Asuman Ozdaglar, Pablo A. Parrilo

Journal:

International Journal of Game Theory

Year:

2011

Language:

english

File:

PDF, 282 KB

english, 2011

33

Computing sum of squares decompositions with rational coefficients

Helfried Peyrl, Pablo A. Parrilo

Journal:

Theoretical Computer Science

Year:

2008

Language:

english

File:

PDF, 739 KB

english, 2008

34

A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs

João Gouveia, Monique Laurent, Pablo A. Parrilo, Rekha Thomas

Journal:

Mathematical Programming

Year:

2012

Language:

english

File:

PDF, 297 KB

english, 2012

35

Efficient classification of complete parameter regions based on semidefinite programming

Lars Kuepfer, Uwe Sauer, Pablo A Parrilo

Journal:

BMC Bioinformatics

Year:

2007

Language:

english

File:

PDF, 402 KB

english, 2007

36

Correlated equilibria in continuous games: Characterization and computation

Noah D. Stein, Pablo A. Parrilo, Asuman Ozdaglar

Journal:

Games and Economic Behavior

Year:

2011

Language:

english

File:

PDF, 350 KB

english, 2011

37

Theta Bodies for Polynomial Ideals

Gouveia, João, Parrilo, Pablo A., Thomas, Rekha R.

Journal:

SIAM Journal on Optimization

Year:

2010

Language:

english

File:

PDF, 389 KB

english, 2010

38

Separable and low-rank continuous games

Noah D. Stein, Asuman Ozdaglar, Pablo A. Parrilo

Journal:

International Journal of Game Theory

Year:

2008

Language:

english

File:

PDF, 384 KB

english, 2008

39

Lifts of Convex Sets and Cone Factorizations

Gouveia, João, Parrilo, Pablo A., Thomas, Rekha R.

Journal:

Mathematics of Operations Research

Year:

2013

Language:

english

File:

PDF, 555 KB

english, 2013

40

A convex polynomial that is not sos-convex

Amir Ali Ahmadi, Pablo A. Parrilo

Journal:

Mathematical Programming

Year:

2012

Language:

english

File:

PDF, 233 KB

english, 2012

41

A Complete Characterization of the Gap between Convexity and SOS-Convexity

Ahmadi, Amir Ali, Parrilo, Pablo A.

Journal:

SIAM Journal on Optimization

Year:

2013

Language:

english

File:

PDF, 306 KB

english, 2013

42

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

Ahmadi, Amir Ali, Jungers, Raphaël M., Parrilo, Pablo A., Roozbehani, Mardavij

Journal:

SIAM Journal on Control and Optimization

Year:

2014

Language:

english

File:

PDF, 1.28 MB

english, 2014

43

Semidefinite Programming Relaxations and Algebraic Optimization in Control

Parrilo, Pablo A., Lall, Sanjay

Journal:

European Journal of Control

Year:

2003

Language:

english

File:

PDF, 182 KB

english, 2003

44

Dynamics in near-potential games

Candogan, Ozan, Ozdaglar, Asuman, Parrilo, Pablo A.

Journal:

Games and Economic Behavior

Year:

2013

Language:

english

File:

PDF, 579 KB

english, 2013

45

[IEEE 2013 IEEE 52nd Annual Conference on Decision and Control (CDC) - Firenze (2013.12.10-2013.12.13)] 52nd IEEE Conference on Decision and Control - Diagonal and low-rank decompositions and fitting ellipsoids to random points

Saunderson, James, Parrilo, Pablo A., Willsky, Alan S.

Year:

2013

Language:

english

File:

PDF, 365 KB

english, 2013

46

[IEEE 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC) - Shanghai, China (2009.12.15-2009.12.18)] Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference - A poset framework to model decentralized control problems

Shah, Parikshit, Parrilo, Pablo A.

Year:

2009

Language:

english

File:

PDF, 843 KB

english, 2009

47

[IEEE 2008 47th IEEE Conference on Decision and Control - Cancun, Mexico (2008.12.9-2008.12.11)] 2008 47th IEEE Conference on Decision and Control - A Partial order approach to decentralized control

Shah, Parikshit, Parrilo, Pablo A.

Year:

2008

Language:

english

File:

PDF, 211 KB

english, 2008

48

[IEEE 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011) - Orlando, FL, USA (2011.12.12-2011.12.15)] IEEE Conference on Decision and Control and European Control Conference - An optimal controller architecture for poset-causal systems

Shah, Parikshit, Parrilo, Pablo A.

Year:

2011

Language:

english

File:

PDF, 469 KB

english, 2011

49

[IEEE 2012 46th Annual Conference on Information Sciences and Systems (CISS) - Princeton, NJ, USA (2012.03.21-2012.03.23)] 2012 46th Annual Conference on Information Sciences and Systems (CISS) - Convex graph invariants

Chandrasekaran, Venkat, Parrilo, Pablo A., Willsky, Alan S.

Year:

2012

Language:

english

File:

PDF, 235 KB

english, 2012

50

[IEEE 2007 46th IEEE Conference on Decision and Control - New Orleans, LA, USA (2007.12.12-2007.12.14)] 2007 46th IEEE Conference on Decision and Control - A theorem of the alternative for SOS Lyapunov functions

Peyrl, Helfried, Parrilo, Pablo A.

Year:

2007

Language:

english

File:

PDF, 454 KB

english, 2007