Edit Profile Parrilo, Pablo A. Compute Distance To: Compute Author ID: parrilo.pablo-a Published as: Parillo, Pablo; Parillo, Pablo A.; Parrilo, P.; Parrilo, P. A.; Parrilo, Pablo; Parrilo, Pablo A. External Links: ORCID Documents Indexed: 90 Publications since 1998, including 2 Books all top 5 Co-Authors 6 single-authored 10 Ozdaglar, Asuman E. 8 Thomas, Rekha R. 7 Ahmadi, Amir Ali 7 Fawzi, Hamza 7 Saunderson, James 7 Willsky, Alan Steven 6 Chandrasekaran, Venkat 6 Jungers, Raphaël M. 5 Cifuentes, Diego 5 Gouveia, Joao 3 Candogan, Ozan 3 Gürbüzbalaban, Mert 3 Laurent, Monique 3 Legat, Benoît 3 Roozbehani, Mardavij 3 Sánchez Peña, Ricardo S. 3 Stein, Noah D. 3 Sturmfels, Bernd 3 Sznaier, Mario 2 Bertsimas, Dimitris John 2 Blekherman, Grigoriy 2 Boyd, Stephen Poythress 2 de Klerk, Etienne 2 Diaconis, Persi Warren 2 Iancu, Dan Andrei 2 Jadbabaie, Ali 2 Lall, Sanjay 2 Permenter, Frank 2 Prajna, Stephen 2 Recht, Benjamin 2 Xiao, Lin 1 Altschuler, Jason M. 1 Amishima, Takeshi 1 Aylward, Erin M. 1 Cogill, Randy 1 De Loera, Jesús A. 1 Fazel, Maryam 1 Fotiou, Ioannis A. 1 Freund, Robert M. 1 Gatermann, Karin 1 Inanc, Tamer 1 Kahle, Thomas 1 Khatri, Sven 1 Kim, Kwang-Ki K. 1 Kubjas, Kaie 1 Lasserre, Jean-Bernard 1 Letchford, Adam N. 1 Lewis, Adrian S. 1 Malkin, Peter N. 1 Mazzaro, Maria Cecilia 1 Men, Han 1 Menache, Ishai 1 Misra, Sidhant 1 Mitter, Sanjoy K. 1 Morari, Manfred 1 Nedić, Angelia 1 Nguyen, Ngoc Cuong 1 Nie, Jiawang 1 Olshevsky, Alex 1 Papachristodoulou, Antonis 1 Peraire, Jaime 1 Peretz, Ronen 1 Peyrl, Helfried 1 Ramana, Motakuri V. 1 Rantzer, Anders 1 Robertson, Aaron 1 Robinson, Richard Z. 1 Rostalski, Philipp 1 Sanghavi, Sujay 1 Saracino, Dan 1 Seiler, Peter J. 1 Shah, Parikshit 1 Slotine, Jean-Jacques E. 1 Steurer, David 1 Tanaka, Takashi 1 Tierno, Jorge E. 1 Tsitsiklis, John N. all top 5 Serials 14 Mathematical Programming. Series A. Series B 10 IEEE Transactions on Automatic Control 9 SIAM Journal on Optimization 4 Automatica 4 Mathematics of Operations Research 3 SIAM Journal on Control and Optimization 2 International Journal of Control 2 The Annals of Statistics 2 International Journal of Game Theory 2 Theoretical Computer Science 2 Games and Economic Behavior 2 Linear Algebra and its Applications 2 SIAM Review 2 Foundations of Computational Mathematics 1 IEEE Transactions on Information Theory 1 Journal of Computational Physics 1 Journal of Combinatorial Theory. Series A 1 Journal of Pure and Applied Algebra 1 Operations Research 1 Proceedings of the American Mathematical Society 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 SIAM Journal on Matrix Analysis and Applications 1 European Journal of Control 1 Internet Mathematics 1 Proceedings of Symposia in Applied Mathematics 1 MOS/SIAM Series on Optimization 1 The Journal of Software for Algebra and Geometry 1 SIAM Journal on Applied Algebra and Geometry all top 5 Fields 64 Operations research, mathematical programming (90-XX) 28 Systems theory; control (93-XX) 17 Convex and discrete geometry (52-XX) 17 Computer science (68-XX) 12 Algebraic geometry (14-XX) 10 Numerical analysis (65-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Combinatorics (05-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Commutative algebra (13-XX) 4 Number theory (11-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 3 Statistics (62-XX) 2 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 79 Publications have been cited 2,138 times in 1,626 Documents Cited by ▼ Year ▼ Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. Zbl 1198.90321Recht, Benjamin; Fazel, Maryam; Parrilo, Pablo A. 370 2010 Semidefinite programming relaxations for semialgebraic problems. Zbl 1043.14018Parrilo, Pablo A. 260 2003 Constrained consensus and optimization in multi-agent networks. Zbl 1368.90143Nedić, Angelia; Ozdaglar, Asuman; Parrilo, Pablo A. 135 2010 Rank-sparsity incoherence for matrix decomposition. Zbl 1226.90067Chandrasekaran, Venkat; Sanghavi, Sujay; Parrilo, Pablo A.; Willsky, Alan S. 114 2011 The convex geometry of linear inverse problems. Zbl 1280.52008Chandrasekaran, Venkat; Recht, Benjamin; Parrilo, Pablo A.; Willsky, Alan S. 105 2012 Semidefinite optimization and convex algebraic geometry. Zbl 1260.90006Blekherman, Grigoriy (ed.); Parrilo, Pablo A. (ed.); Thomas, Rekha R. (ed.) 95 2013 Minimizing polynomial functions. Zbl 1099.13516Parrilo, Pablo A.; Sturmfels, Bernd 84 2003 Symmetry groups, semidefinite programs, and sums of squares. Zbl 1108.13021Gatermann, Karin; Parrilo, Pablo A. 75 2004 Lifts of convex sets and cone factorizations. Zbl 1291.90172Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 56 2013 The Lax conjecture is true. Zbl 1073.90029Lewis, A. S.; Parrilo, P. A.; Ramana, M. V. 54 2005 Latent variable graphical model selection via convex optimization. Zbl 1257.62061Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 53 2012 Theta bodies for polynomial ideals. Zbl 1213.90190Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 46 2010 Nonlinear control synthesis by convex optimization. Zbl 1365.93164Prajna, Stephen; Parrilo, Pablo A.; Rantzer, Anders 39 2004 Optimality of affine policies in multistage robust optimization. Zbl 1218.90216Bertsimas, Dimitris; Iancu, Dan A.; Parrilo, Pablo A. 38 2010 A PTAS for the minimization of polynomials of fixed degree over the simplex. Zbl 1115.90042De Klerk, Etienne; Laurent, Monique; Parrilo, Pablo A. 34 2006 SOSTOOLS and its control applications. Zbl 1119.93302Prajna, Stephen; Papachristodoulou, Antonis; Seiler, Peter; Parrilo, Pablo A. 31 2005 A hierarchy of near-optimal policies for multistage adaptive optimization. Zbl 1368.93336Bertsimas, Dimitris; Iancu, Dan Andrei; Parrilo, Pablo A. 26 2011 Flows and decompositions of games: harmonic and potential games. Zbl 1239.91006Candogan, Ozan; Menache, Ishai; Ozdaglar, Asuman; Parrilo, Pablo A. 25 2011 Approximation of the joint spectral radius using sum of squares. Zbl 1151.65032Parrilo, Pablo A.; Jadbabaie, Ali 25 2008 Positive semidefinite rank. Zbl 1327.90174Fawzi, Hamza; Gouveia, João; Parrilo, Pablo A.; Robinson, Richard Z.; Thomas, Rekha R. 24 2015 Computing sum of squares decompositions with rational coefficients. Zbl 1156.65062Peyrl, Helfried; Parrilo, Pablo A. 24 2008 NP-hardness of deciding convexity of quartic polynomials and related problems. Zbl 1274.90516Ahmadi, Amir Ali; Olshevsky, Alex; Parrilo, Pablo A.; Tsitsiklis, John N. 23 2013 A complete characterization of the gap between convexity and sos-convexity. Zbl 1295.52009Ahmadi, Amir Ali; Parrilo, Pablo A. 21 2013 Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming. Zbl 1283.93217Aylward, Erin M.; Parrilo, Pablo A.; Slotine, Jean-Jacques E. 20 2008 Joint spectral radius and path-complete graph Lyapunov functions. Zbl 1292.93093Ahmadi, Amir Ali; Jungers, Raphaël M.; Parrilo, Pablo A.; Roozbehani, Mardavij 19 2014 A convex polynomial that is not sos-convex. Zbl 1254.90159Ahmadi, Amir Ali; Parrilo, Pablo A. 19 2012 Rejoinder: Latent variable graphical model selection via convex optimization. Zbl 1288.62085Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 18 2012 Semidefinite programming relaxations and algebraic optimization in control. Zbl 1293.93302Parrilo, Pablo A.; Lall, Sanjay 18 2003 Symmetry analysis of reversible Markov chains. Zbl 1087.60057Boyd, Stephen; Diaconis, Persi; Parrilo, Pablo; Xiao, Lin 17 2005 Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone. Zbl 1405.90098Permenter, Frank; Parrilo, Pablo 16 2018 On the convergence rate of incremental aggregated gradient algorithms. Zbl 1366.90195Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. 15 2017 Dynamics in near-potential games. Zbl 1282.91048Candogan, Ozan; Ozdaglar, Asuman; Parrilo, Pablo A. 14 2013 Equivariant semidefinite lifts and sum-of-squares hierarchies. Zbl 1327.90175Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 13 2015 Fastest mixing Markov chain on graphs with symmetries. Zbl 1189.05072Boyd, Stephen; Diaconis, Persi; Parrilo, Pablo; Xiao, Lin 12 2009 A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs. Zbl 1262.90123Gouveia, João; Laurent, Monique; Parrilo, Pablo A.; Thomas, Rekha 11 2012 Semidefinite descriptions of the convex hull of rotation matrices. Zbl 1317.90231Saunderson, J.; Parrilo, P. A.; Willsky, A. S. 9 2015 Semidefinite representation of the \(k\)-ellipse. Zbl 1171.90498Nie, Jiawang; Parrilo, Pablo A.; Sturmfels, Bernd 9 2008 Exploiting algebraic structure in sum of squares programs. Zbl 1070.90081Parrilo, Pablo A. 9 2005 Mixed time/frequency-domain based robust identification. Zbl 0963.93017Parrilo, P. A.; Sznaier, M.; Sánchez Peña, R. S.; Inanc, T. 9 1998 Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank. Zbl 1346.90662Fawzi, Hamza; Parrilo, Pablo A. 8 2016 Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones. Zbl 1327.90180Saunderson, James; Parrilo, Pablo A. 8 2015 \(\mathcal H_2\)-optimal decentralized control over posets: a state-space solution for state-feedback. Zbl 1369.93045Shah, Parikshit; Parrilo, Pablo A. 8 2013 Diagonal and low-rank matrix decompositions, correlation matrices, and ellipsoid fitting. Zbl 1270.90043Saunderson, J.; Chandrasekaran, V.; Parrilo, P. A.; Willsky, A. S. 8 2012 On the equivalence of algebraic approaches to the minimization of forms on the simplex. Zbl 1138.90439de Klerk, Etienne; Laurent, Monique; Parillo, Pablo 8 2005 Equivariant semidefinite lifts of regular polygons. Zbl 1364.90245Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 7 2017 Lower bounds on nonnegative rank via nonnegative nuclear norms. Zbl 1327.90202Fawzi, Hamza; Parrilo, Pablo A. 7 2015 Sparse sums of squares on finite abelian groups and improved semidefinite lifts. Zbl 1387.90180Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 6 2016 Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs. Zbl 1364.93376Ahmadi, Amir Ali; Jungers, Raphaël; Parrilo, Pablo A.; Roozbehani, Mardavij 6 2011 Parametric optimization and optimal control using algebraic geometry methods. Zbl 1133.93337Fotiou, I. A.; Rostalski, P.; Parrilo, P. A.; Morari, M. 6 2006 An efficient tree decomposition method for permanents and mixed discriminants. Zbl 1329.15020Cifuentes, Diego; Parrilo, Pablo A. 5 2016 A globally convergent incremental Newton method. Zbl 1316.49033Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. 5 2015 Polynomial optimization, sums of squares, and applications. Zbl 1360.90194Parrilo, Pablo A. 5 2013 Convex graph invariants. Zbl 1250.05091Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 5 2012 Computation with polynomial equations and inequalities arising in combinatorial optimization. Zbl 1242.90191De Loera, Jesús A.; Malkin, Peter N.; Parrilo, Pablo A. 5 2012 On cone-invariant linear matrix inequalities. Zbl 0988.93029Parrilo, Pablo A.; Khatri, Sven 5 2000 Sampling algebraic varieties for sum of squares programs. Zbl 1386.90099Cifuentes, Diego; Parrilo, Pablo A. 4 2017 Exploiting chordal structure in polynomial ideals: a Gröbner bases approach. Zbl 1353.13033Cifuentes, Diego; Parrilo, Pablo A. 4 2016 Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. Zbl 1192.82104Men, H.; Nguyen, N. C.; Freund, R. M.; Parrilo, P. A.; Peraire, J. 4 2010 Separable and low-rank continuous games. Zbl 1160.91003Stein, Noah D.; Ozdaglar, Asuman; Parrilo, Pablo A. 4 2008 On the asymptotic minimum number of monochromatic 3-term arithmetic progressions. Zbl 1210.05172Parrilo, Pablo A.; Robertson, Aaron; Saracino, Dan 4 2008 Approximation of the joint spectral radius of a set of matrices using sum of squares. Zbl 1221.65098Parrilo, Pablo A.; Jadbabaie, Ali 4 2007 Approximate cone factorizations and lifts of polytopes. Zbl 1319.52010Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 3 2015 Correlated equilibria in continuous games: characterization and computation. Zbl 1208.91018Stein, Noah D.; Parrilo, Pablo A.; Ozdaglar, Asuman 3 2011 How to flatten a soccer ball. Zbl 1406.14042Kubjas, Kaie; Parrilo, Pablo A.; Sturmfels, Bernd 2 2017 A characterization of Lyapunov inequalities for stability of switched systems. Zbl 1369.93532Jungers, Raphaël M.; Ahmadi, Amir Ali; Parrilo, Pablo A.; Roozbehani, Mardavij 2 2017 Semidefinite programming approach to Gaussian sequential rate-distortion trade-offs. Zbl 1366.90159Tanaka, Takashi; Kim, Kwang-Ki K.; Parrilo, Pablo A.; Mitter, Sanjoy K. 2 2017 Weighted \(\ell_1\)-minimization for generalized non-uniform sparse model. Zbl 1359.94139Misra, Sidhant; Parrilo, Pablo A. 2 2015 Structured semidefinite programs for the control of symmetric systems. Zbl 1283.93116Cogill, Randy; Lall, Sanjay; Parrilo, Pablo A. 2 2008 Convergence rate of incremental gradient and incremental Newton methods. Zbl 1428.90119Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. 1 2019 Semidefinite approximations of the matrix logarithm. Zbl 1411.90254Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 1 2019 Chordal networks of polynomial ideals. Zbl 1444.13037Cifuentes, Diego; Parrilo, Pablo A. 1 2017 Generating unstable trajectories for switched systems via dual sum-of-squares techniques. Zbl 1364.93315Legat, Benoît; Jungers, Raphaël M.; Parrilo, Pablo A. 1 2016 Iterative auction design for tree valuations. Zbl 1329.91046Candogan, Ozan; Ozdaglar, Asuman; Parrilo, Pablo A. 1 2015 Semidefinite optimization. Zbl 1360.90193Parrilo, Pablo A. 1 2013 What is convex algebraic geometry? Zbl 1360.90186Blekherman, Grigoriy; Parrilo, Pablo A.; Thomas, Rekha R. 1 2013 Structure of extreme correlated equilibria: A zero-sum example and its implications. Zbl 1233.91051Stein, Noah D.; Ozdaglar, Asuman; Parrilo, Pablo A. 1 2011 An inequality for circle packings proved by semidefinite programming. Zbl 1059.51020Parrilo, Pablo A.; Peretz, Ronen 1 2004 A convex approach to robust \({\mathcal H}_{2}\) performance analysis. Zbl 1012.93023Sznaier, M.; Amishima, T.; Parrilo, P. A.; Tierno, J. 1 2002 A parametric extension of mixed time/frequency robust identification. Zbl 0958.93028Parrilo, Pablo A.; Sánchez Peña, Ricardo S.; Sznaier, Mario 1 1999 Convergence rate of incremental gradient and incremental Newton methods. Zbl 1428.90119Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. 1 2019 Semidefinite approximations of the matrix logarithm. Zbl 1411.90254Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 1 2019 Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone. Zbl 1405.90098Permenter, Frank; Parrilo, Pablo 16 2018 On the convergence rate of incremental aggregated gradient algorithms. Zbl 1366.90195Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. 15 2017 Equivariant semidefinite lifts of regular polygons. Zbl 1364.90245Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 7 2017 Sampling algebraic varieties for sum of squares programs. Zbl 1386.90099Cifuentes, Diego; Parrilo, Pablo A. 4 2017 How to flatten a soccer ball. Zbl 1406.14042Kubjas, Kaie; Parrilo, Pablo A.; Sturmfels, Bernd 2 2017 A characterization of Lyapunov inequalities for stability of switched systems. Zbl 1369.93532Jungers, Raphaël M.; Ahmadi, Amir Ali; Parrilo, Pablo A.; Roozbehani, Mardavij 2 2017 Semidefinite programming approach to Gaussian sequential rate-distortion trade-offs. Zbl 1366.90159Tanaka, Takashi; Kim, Kwang-Ki K.; Parrilo, Pablo A.; Mitter, Sanjoy K. 2 2017 Chordal networks of polynomial ideals. Zbl 1444.13037Cifuentes, Diego; Parrilo, Pablo A. 1 2017 Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank. Zbl 1346.90662Fawzi, Hamza; Parrilo, Pablo A. 8 2016 Sparse sums of squares on finite abelian groups and improved semidefinite lifts. Zbl 1387.90180Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 6 2016 An efficient tree decomposition method for permanents and mixed discriminants. Zbl 1329.15020Cifuentes, Diego; Parrilo, Pablo A. 5 2016 Exploiting chordal structure in polynomial ideals: a Gröbner bases approach. Zbl 1353.13033Cifuentes, Diego; Parrilo, Pablo A. 4 2016 Generating unstable trajectories for switched systems via dual sum-of-squares techniques. Zbl 1364.93315Legat, Benoît; Jungers, Raphaël M.; Parrilo, Pablo A. 1 2016 Positive semidefinite rank. Zbl 1327.90174Fawzi, Hamza; Gouveia, João; Parrilo, Pablo A.; Robinson, Richard Z.; Thomas, Rekha R. 24 2015 Equivariant semidefinite lifts and sum-of-squares hierarchies. Zbl 1327.90175Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A. 13 2015 Semidefinite descriptions of the convex hull of rotation matrices. Zbl 1317.90231Saunderson, J.; Parrilo, P. A.; Willsky, A. S. 9 2015 Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones. Zbl 1327.90180Saunderson, James; Parrilo, Pablo A. 8 2015 Lower bounds on nonnegative rank via nonnegative nuclear norms. Zbl 1327.90202Fawzi, Hamza; Parrilo, Pablo A. 7 2015 A globally convergent incremental Newton method. Zbl 1316.49033Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. 5 2015 Approximate cone factorizations and lifts of polytopes. Zbl 1319.52010Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 3 2015 Weighted \(\ell_1\)-minimization for generalized non-uniform sparse model. Zbl 1359.94139Misra, Sidhant; Parrilo, Pablo A. 2 2015 Iterative auction design for tree valuations. Zbl 1329.91046Candogan, Ozan; Ozdaglar, Asuman; Parrilo, Pablo A. 1 2015 Joint spectral radius and path-complete graph Lyapunov functions. Zbl 1292.93093Ahmadi, Amir Ali; Jungers, Raphaël M.; Parrilo, Pablo A.; Roozbehani, Mardavij 19 2014 Semidefinite optimization and convex algebraic geometry. Zbl 1260.90006Blekherman, Grigoriy (ed.); Parrilo, Pablo A. (ed.); Thomas, Rekha R. (ed.) 95 2013 Lifts of convex sets and cone factorizations. Zbl 1291.90172Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 56 2013 NP-hardness of deciding convexity of quartic polynomials and related problems. Zbl 1274.90516Ahmadi, Amir Ali; Olshevsky, Alex; Parrilo, Pablo A.; Tsitsiklis, John N. 23 2013 A complete characterization of the gap between convexity and sos-convexity. Zbl 1295.52009Ahmadi, Amir Ali; Parrilo, Pablo A. 21 2013 Dynamics in near-potential games. Zbl 1282.91048Candogan, Ozan; Ozdaglar, Asuman; Parrilo, Pablo A. 14 2013 \(\mathcal H_2\)-optimal decentralized control over posets: a state-space solution for state-feedback. Zbl 1369.93045Shah, Parikshit; Parrilo, Pablo A. 8 2013 Polynomial optimization, sums of squares, and applications. Zbl 1360.90194Parrilo, Pablo A. 5 2013 Semidefinite optimization. Zbl 1360.90193Parrilo, Pablo A. 1 2013 What is convex algebraic geometry? Zbl 1360.90186Blekherman, Grigoriy; Parrilo, Pablo A.; Thomas, Rekha R. 1 2013 The convex geometry of linear inverse problems. Zbl 1280.52008Chandrasekaran, Venkat; Recht, Benjamin; Parrilo, Pablo A.; Willsky, Alan S. 105 2012 Latent variable graphical model selection via convex optimization. Zbl 1257.62061Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 53 2012 A convex polynomial that is not sos-convex. Zbl 1254.90159Ahmadi, Amir Ali; Parrilo, Pablo A. 19 2012 Rejoinder: Latent variable graphical model selection via convex optimization. Zbl 1288.62085Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 18 2012 A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs. Zbl 1262.90123Gouveia, João; Laurent, Monique; Parrilo, Pablo A.; Thomas, Rekha 11 2012 Diagonal and low-rank matrix decompositions, correlation matrices, and ellipsoid fitting. Zbl 1270.90043Saunderson, J.; Chandrasekaran, V.; Parrilo, P. A.; Willsky, A. S. 8 2012 Convex graph invariants. Zbl 1250.05091Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. 5 2012 Computation with polynomial equations and inequalities arising in combinatorial optimization. Zbl 1242.90191De Loera, Jesús A.; Malkin, Peter N.; Parrilo, Pablo A. 5 2012 Rank-sparsity incoherence for matrix decomposition. Zbl 1226.90067Chandrasekaran, Venkat; Sanghavi, Sujay; Parrilo, Pablo A.; Willsky, Alan S. 114 2011 A hierarchy of near-optimal policies for multistage adaptive optimization. Zbl 1368.93336Bertsimas, Dimitris; Iancu, Dan Andrei; Parrilo, Pablo A. 26 2011 Flows and decompositions of games: harmonic and potential games. Zbl 1239.91006Candogan, Ozan; Menache, Ishai; Ozdaglar, Asuman; Parrilo, Pablo A. 25 2011 Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs. Zbl 1364.93376Ahmadi, Amir Ali; Jungers, Raphaël; Parrilo, Pablo A.; Roozbehani, Mardavij 6 2011 Correlated equilibria in continuous games: characterization and computation. Zbl 1208.91018Stein, Noah D.; Parrilo, Pablo A.; Ozdaglar, Asuman 3 2011 Structure of extreme correlated equilibria: A zero-sum example and its implications. Zbl 1233.91051Stein, Noah D.; Ozdaglar, Asuman; Parrilo, Pablo A. 1 2011 Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. Zbl 1198.90321Recht, Benjamin; Fazel, Maryam; Parrilo, Pablo A. 370 2010 Constrained consensus and optimization in multi-agent networks. Zbl 1368.90143Nedić, Angelia; Ozdaglar, Asuman; Parrilo, Pablo A. 135 2010 Theta bodies for polynomial ideals. Zbl 1213.90190Gouveia, João; Parrilo, Pablo A.; Thomas, Rekha R. 46 2010 Optimality of affine policies in multistage robust optimization. Zbl 1218.90216Bertsimas, Dimitris; Iancu, Dan A.; Parrilo, Pablo A. 38 2010 Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. Zbl 1192.82104Men, H.; Nguyen, N. C.; Freund, R. M.; Parrilo, P. A.; Peraire, J. 4 2010 Fastest mixing Markov chain on graphs with symmetries. Zbl 1189.05072Boyd, Stephen; Diaconis, Persi; Parrilo, Pablo; Xiao, Lin 12 2009 Approximation of the joint spectral radius using sum of squares. Zbl 1151.65032Parrilo, Pablo A.; Jadbabaie, Ali 25 2008 Computing sum of squares decompositions with rational coefficients. Zbl 1156.65062Peyrl, Helfried; Parrilo, Pablo A. 24 2008 Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming. Zbl 1283.93217Aylward, Erin M.; Parrilo, Pablo A.; Slotine, Jean-Jacques E. 20 2008 Semidefinite representation of the \(k\)-ellipse. Zbl 1171.90498Nie, Jiawang; Parrilo, Pablo A.; Sturmfels, Bernd 9 2008 Separable and low-rank continuous games. Zbl 1160.91003Stein, Noah D.; Ozdaglar, Asuman; Parrilo, Pablo A. 4 2008 On the asymptotic minimum number of monochromatic 3-term arithmetic progressions. Zbl 1210.05172Parrilo, Pablo A.; Robertson, Aaron; Saracino, Dan 4 2008 Structured semidefinite programs for the control of symmetric systems. Zbl 1283.93116Cogill, Randy; Lall, Sanjay; Parrilo, Pablo A. 2 2008 Approximation of the joint spectral radius of a set of matrices using sum of squares. Zbl 1221.65098Parrilo, Pablo A.; Jadbabaie, Ali 4 2007 A PTAS for the minimization of polynomials of fixed degree over the simplex. Zbl 1115.90042De Klerk, Etienne; Laurent, Monique; Parrilo, Pablo A. 34 2006 Parametric optimization and optimal control using algebraic geometry methods. Zbl 1133.93337Fotiou, I. A.; Rostalski, P.; Parrilo, P. A.; Morari, M. 6 2006 The Lax conjecture is true. Zbl 1073.90029Lewis, A. S.; Parrilo, P. A.; Ramana, M. V. 54 2005 SOSTOOLS and its control applications. Zbl 1119.93302Prajna, Stephen; Papachristodoulou, Antonis; Seiler, Peter; Parrilo, Pablo A. 31 2005 Symmetry analysis of reversible Markov chains. Zbl 1087.60057Boyd, Stephen; Diaconis, Persi; Parrilo, Pablo; Xiao, Lin 17 2005 Exploiting algebraic structure in sum of squares programs. Zbl 1070.90081Parrilo, Pablo A. 9 2005 On the equivalence of algebraic approaches to the minimization of forms on the simplex. Zbl 1138.90439de Klerk, Etienne; Laurent, Monique; Parillo, Pablo 8 2005 Symmetry groups, semidefinite programs, and sums of squares. Zbl 1108.13021Gatermann, Karin; Parrilo, Pablo A. 75 2004 Nonlinear control synthesis by convex optimization. Zbl 1365.93164Prajna, Stephen; Parrilo, Pablo A.; Rantzer, Anders 39 2004 An inequality for circle packings proved by semidefinite programming. Zbl 1059.51020Parrilo, Pablo A.; Peretz, Ronen 1 2004 Semidefinite programming relaxations for semialgebraic problems. Zbl 1043.14018Parrilo, Pablo A. 260 2003 Minimizing polynomial functions. Zbl 1099.13516Parrilo, Pablo A.; Sturmfels, Bernd 84 2003 Semidefinite programming relaxations and algebraic optimization in control. Zbl 1293.93302Parrilo, Pablo A.; Lall, Sanjay 18 2003 A convex approach to robust \({\mathcal H}_{2}\) performance analysis. Zbl 1012.93023Sznaier, M.; Amishima, T.; Parrilo, P. A.; Tierno, J. 1 2002 On cone-invariant linear matrix inequalities. Zbl 0988.93029Parrilo, Pablo A.; Khatri, Sven 5 2000 A parametric extension of mixed time/frequency robust identification. Zbl 0958.93028Parrilo, Pablo A.; Sánchez Peña, Ricardo S.; Sznaier, Mario 1 1999 Mixed time/frequency-domain based robust identification. Zbl 0963.93017Parrilo, P. A.; Sznaier, M.; Sánchez Peña, R. S.; Inanc, T. 9 1998 all cited Publications top 5 cited Publications all top 5 Cited by 2,603 Authors 34 Parrilo, Pablo A. 23 Nie, Jiawang 20 de Klerk, Etienne 17 Jeyakumar, Vaithilingam 17 Klep, Igor 16 Laurent, Monique 14 Gouveia, Joao 14 Li, Guoyin 12 Ahmadi, Amir Ali 12 Sturmfels, Bernd 11 Bertsimas, Dimitris John 11 Chandrasekaran, Venkat 11 Fawzi, Hamza 11 Helton, John William 11 Hong, Yiguang 11 Lasserre, Jean-Bernard 11 Ma, Shiqian 11 Thomas, Rekha R. 11 Yuan, Xiaoming 10 Blekherman, Grigoriy 10 Qi, Liqun 10 Rauhut, Holger 10 Saunderson, James 10 Tunçel, Levent 9 den Hertog, Dick 9 Han, Deren 9 Jungers, Raphaël M. 8 Cheng, Daizhan 8 Goldfarb, Donald 8 Ozdaglar, Asuman E. 8 Povh, Janez 8 Recht, Benjamin 8 Shi, Guodong 8 Sotirov, Renata 8 Sun, Defeng 8 Theobald, Thorsten 8 Toh, Kimchuan 8 Wu, Zhiyou 8 Xiu, Naihua 8 Yin, Wotao 7 Brändén, Petter 7 Chien, Mao-Ting 7 Chuong, Thai Doan 7 Gaubert, Stéphane 7 Kozyakin, Viktor Sergeevich 7 Kurpisz, Adam 7 Mastrolilli, Monaldo 7 McCullough, Scott A. 7 Muramatsu, Masakazu 7 Nakazato, Hiroshi 7 Pasechnik, Dmitrii V. 7 Pokutta, Sebastian 7 Robinson, Richard Z. 7 Rustem, Berc 7 Shitov, Yaroslav Nikolaevich 7 Velasco, Mauricio 7 Vera, Juan-Carlos 7 Waki, Hayato 7 Zhang, Shuzhong 6 Anjos, Miguel F. 6 Bi, Shujun 6 Cafuta, Kristijan 6 Cai, Jian-Feng 6 Cai, Tony Tony 6 Cerone, Vito 6 Ding, Chao 6 Georghiou, Angelos 6 Gillis, Nicolas 6 Hall, Georgina 6 Hu, ShengLong 6 Huang, Zheng-Hai 6 Kuhn, Daniel 6 Li, Jueyou 6 Nedić, Angelia 6 Netzer, Tim 6 Packard, Andrew K. 6 Pan, Shaohua 6 Phạm Tiên So’n 6 Regruto, Diego 6 Safey El Din, Mohab 6 Sanyal, Raman 6 She, Zhikun 6 Sinn, Rainer 6 Sun, Zhao 6 Tian, Yongge 6 Wen, Zaiwen 6 Yuan, Deming 5 Allamigeon, Xavier 5 Aravkin, Aleksandr Y. 5 Bomze, Immanuel M. 5 Braun, Gábor 5 Cevher, Volkan 5 Chernyshenko, Sergei I. 5 Chi, Yuejie 5 De Loera, Jesús A. 5 de Wolff, Timo 5 Fadili, Jalal M. 5 Fiorini, Samuel 5 Giesl, Peter 5 Girard, Antoine ...and 2,503 more Authors all top 5 Cited in 290 Serials 142 Mathematical Programming. 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Series A 5 Optimization 5 Multidimensional Systems and Signal Processing 5 International Journal of Computer Vision 5 Bernoulli 5 The Journal of Fourier Analysis and Applications 5 Inverse Problems and Imaging 5 Asian Journal of Control 5 Statistics and Computing 4 Communications in Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Asia-Pacific Journal of Operational Research 4 Journal of Mathematical Imaging and Vision 4 Formal Methods in System Design 4 Advances in Computational Mathematics 4 Nonlinear Dynamics 4 Abstract and Applied Analysis 4 Optimization and Engineering 4 International Journal of Wavelets, Multiresolution and Information Processing 4 Computational Management Science 4 Journal of Industrial and Management Optimization 4 Frontiers of Mathematics in China 3 Discrete Applied Mathematics 3 Journal of Computational Physics 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 Fuzzy Sets and Systems 3 Journal of Algebra 3 Journal of the American Statistical Association 3 Mathematische Zeitschrift 3 Transactions of the American Mathematical Society 3 Advances in Applied Mathematics 3 Applied Numerical Mathematics 3 Journal of Complexity 3 Statistical Science 3 Computers & Operations Research 3 Journal of Automated Reasoning 3 Applied Mathematics Letters 3 Journal of the American Mathematical Society 3 The Annals of Applied Probability 3 Discrete Event Dynamic Systems 3 Applied Mathematical Modelling ...and 190 more Serials all top 5 Cited in 54 Fields 835 Operations research, mathematical programming (90-XX) 313 Systems theory; control (93-XX) 295 Numerical analysis (65-XX) 238 Computer science (68-XX) 222 Linear and multilinear algebra; matrix theory (15-XX) 149 Statistics (62-XX) 123 Information and communication theory, circuits (94-XX) 116 Algebraic geometry (14-XX) 110 Calculus of variations and optimal control; optimization (49-XX) 100 Convex and discrete geometry (52-XX) 93 Combinatorics (05-XX) 72 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 60 Commutative algebra (13-XX) 59 Probability theory and stochastic processes (60-XX) 45 Operator theory (47-XX) 32 Field theory and polynomials (12-XX) 31 Quantum theory (81-XX) 30 Number theory (11-XX) 28 Ordinary differential equations (34-XX) 26 Functional analysis (46-XX) 23 Dynamical systems and ergodic theory (37-XX) 20 Partial differential equations (35-XX) 20 Biology and other natural sciences (92-XX) 15 Real functions (26-XX) 15 Approximations and expansions (41-XX) 13 Group theory and generalizations (20-XX) 8 Mathematical logic and foundations (03-XX) 8 Mechanics of particles and systems (70-XX) 7 Functions of a complex variable (30-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Geometry (51-XX) 7 Fluid mechanics (76-XX) 6 Associative rings and algebras (16-XX) 6 Differential geometry (53-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 5 Topological groups, Lie groups (22-XX) 5 Special functions (33-XX) 5 Integral transforms, operational calculus (44-XX) 4 General algebraic systems (08-XX) 4 Nonassociative rings and algebras (17-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Optics, electromagnetic theory (78-XX) 3 History and biography (01-XX) 3 Abstract harmonic analysis (43-XX) 3 Manifolds and cell complexes (57-XX) 3 Mechanics of deformable solids (74-XX) 3 Geophysics (86-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Measure and integration (28-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year