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The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem.
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Computing the joint spectral radius
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Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones
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Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones
Jos F Sturm · 1999
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A spectral bundle method for semidefinite programming
Christoph Helmberg and Franz Rendl · 2000
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Global Optimization with Polynomials and the Problem of Moments
Jean-Bernard Lasserre · 2001
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Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Aharon Ben-Tal and Arkadi Nemirovski · 2001
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Global Optimization with Polynomials and the Problem of Moments
Jean-Bernard Lasserre · 2001
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Analysis, graduate stud. math., vol. 14
Elliott H Lieb and Michael Loss · 2001
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Global Optimization with Polynomials and the Problem of Moments
Jean-Bernard Lasserre · 2001
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Factorization of operator-valued polynomials in several non-commuting variables
Scott McCullough · 2001
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Global Optimization with Polynomials and the Problem of Moments
Jean-Bernard Lasserre · 2001
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A Course in Convexity
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Accuracy and Stability of Numerical Algorithms: Second Edition
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“Positive” noncommutative polynomials are sums of squares
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Configuration of separability and tests for multipartite entanglement in Bell-type experiments
Koji Nagata, Masato Koashi, and Nobuyuki Imoto · 2002
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Quadratic Bell inequalities as tests for multipartite entanglement
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On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D Andersen, Cornelis Roos, and Tamas Terlaky · 2003
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On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D Andersen, Cornelis Roos, and Tamas Terlaky · 2003
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On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D Andersen, Cornelis Roos, and Tamas Terlaky · 2003
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On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D Andersen, Cornelis Roos, and Tamas Terlaky · 2003
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Yalmip : A toolbox for modeling and optimization in MATLAB
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A Positivstellensatz for non-commutative polynomials
J. William Helton and Scott A. McCullough · 2004
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Equivalent forms of the Bessis-Moussa-Villani conjecture
Elliott H. Lieb and Robert Seiringer · 2004
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Yalmip : A toolbox for modeling and optimization in MATLAB
J. Löfberg · 2004
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Symmetry groups, semidefinite programs, and sums of squares
Karin Gatermann and Pablo A Parrilo · 2004
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From coefficients to samples: a new approach to sos optimization
Johan Lofberg and Pablo A Parrilo · 2004
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Yalmip : A toolbox for modeling and optimization in MATLAB
J. Löfberg · 2004
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Detecting Global Optimality and Extracting Solutions in GloptiPoly
D. Henrion and Jean-Bernard Lasserre · 2005
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A polyhedral branch-and-cut approach to global optimization
Mohit Tawarmalani and Nikolaos V Sahinidis · 2005
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Noncommutative sums of squares
Scott McCullough and Mihai Putinar · 2005
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Sparsity in sums of squares of polynomials
Masakazu Kojima, Sunyoung Kim, and Hayato Waki · 2005
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Detecting Global Optimality and Extracting Solutions in GloptiPoly
D. Henrion and Jean-Bernard Lasserre · 2005
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Local minima and convergence in low-rank semidefinite programming
Samuel Burer and Renato DC Monteiro · 2005
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Convergent sdp-relaxations in polynomial optimization with sparsity
Jean B Lasserre · 2006
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Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity
Hayato Waki, Sunyoung Kim, Masakazu Kojima, and Masakazu Muramatsu · 2006
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Convergent sdp-relaxations in polynomial optimization with sparsity
Jean B Lasserre · 2006
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Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity
Hayato Waki, Sunyoung Kim, Masakazu Kojima, and Masakazu Muramatsu · 2006
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Introduction to the flyspeck project
Thomas C. Hales · 2006
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Convergent sdp-relaxations in polynomial optimization with sparsity
Jean B Lasserre · 2006
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Convergent sdp-relaxations in polynomial optimization with sparsity
Jean B Lasserre · 2006
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Convergent sdp-relaxations in polynomial optimization with sparsity
Jean B Lasserre · 2006
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Radial distribution load flow using conic programming
Rabih A Jabr · 2006
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A note on the representation of positive polynomials with structured sparsity
David Grimm, Tim Netzer, and Markus Schweighofer · 2007
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A note on the representation of positive polynomials with structured sparsity
David Grimm, Tim Netzer, and Markus Schweighofer · 2007
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Semidefinite characterization and computation of zero-dimensional real radical ideals
Jean Bernard Lasserre, Monique Laurent, and Philipp Rostalski · 2008
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IEEE Standard for Floating-Point Arithmetic
IEEE · 2008
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A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
Miguel Navascués, Stefano Pironio, and Antonio Acín · 2008
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Algorithm 883: Sparsepop—a sparse semidefinite programming relaxation of polynomial optimization problems
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Semidefinite programming for optimal power flow problems
Xiaoqing Bai, Hua Wei, Katsuki Fujisawa, and Yong Wang · 2008
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Approximation of the joint spectral radius using sum of squares
Pablo A Parrilo and Ali Jadbabaie · 2008
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Computing sum of squares decompositions with rational coefficients
H. Peyrl and P.A. Parrilo · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Amir Beck and Marc Teboulle · 2009
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Block-diagonal semidefinite programming hierarchies for 0/1 programming
Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
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Semidefinite relaxations for certifying robustness to adversarial examples
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Lipschitz regularity of deep neural networks: Analysis and efficient estimation
Aladin Virmaux and Kevin Scaman · 2018
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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
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Towards fast computation of certified robustness for relu networks
Lily Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Luca Daniel, Duane Boning, and Inderjit Dhillon · 2018
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Evaluating the robustness of neural networks: An extreme value theory approach
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Nebojša Gvozdenović, Monique Laurent, and Frank Vallentin · 2009
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Matrix completion problems
Monique Laurent · 2009
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Towards an industrial use of fluctuat on safety-critical avionics software
David Delmas, Eric Goubault, Sylvie Putot, Jean Souyris, Karim Tekkal, and Franck Védrine · 2009
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Engineering systems and free semi-algebraic geometry
Mauricio C. de Oliveira, J. William Helton, Scott A. McCullough, and Mihai Putinar · 2009
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GloptiPoly 3: moments, optimization and semidefinite programming
D. Henrion, Jean-Bernard Lasserre, and J. Löfberg · 2009
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Quantum bounds on Bell inequalities
Károly F. Pál and Tamás Vértesi · 2009
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GloptiPoly 3: moments, optimization and semidefinite programming
D. Henrion, Jean-Bernard Lasserre, and J. Löfberg · 2009
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Efficient neural network robustness certification with general activation functions
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Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
Sander Gribling, David de Laat, and Monique Laurent · 2018
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Tight-and-cheap conic relaxation for the ac optimal power flow problem
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Lasserre hierarchy for large scale polynomial optimization in real and complex variables
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The power grid library for benchmarking AC optimal power flow algorithms
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