A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations
暂无分享,去创建一个
[1] Cyril Cohen,et al. Refinements for Free! , 2013, CPP.
[2] László Lovász,et al. Factoring polynomials with rational coefficients , 1982 .
[3] Makoto Yamashita,et al. A high-performance software package for semidefinite programs: SDPA 7 , 2010 .
[4] Dale Miller,et al. Certified Programs and Proofs , 2012, Lecture Notes in Computer Science.
[5] César A. Muñoz,et al. Formalization of Bernstein Polynomials and Applications to Global Optimization , 2013, Journal of Automated Reasoning.
[6] Siegfried M. Rump,et al. Verification methods: rigorous results using floating-point arithmetic , 2010, Acta Numerica.
[7] B. Borchers. A C library for semidefinite programming , 1999 .
[8] Frédéric Besson,et al. Fast Reflexive Arithmetic Tactics the Linear Case and Beyond , 2006, TYPES.
[9] Thomas C. Hales,et al. Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations , 2013, NASA Formal Methods.
[10] Anton van den Hengel,et al. Semidefinite Programming , 2014, Computer Vision, A Reference Guide.
[11] J. Lasserre. Moments, Positive Polynomials And Their Applications , 2009 .
[12] César A. Muñoz,et al. A Formally Verified Generic Branching Algorithm for Global Optimization , 2013, VSTTE.
[13] Pierre Corbineau,et al. On the Generation of Positivstellensatz Witnesses in Degenerate Cases , 2011, ITP.
[14] Pierre-Yves Strub,et al. Formal proofs of transcendence for e and pi as an application of multivariate and symmetric polynomials , 2015, CPP.
[15] John Harrison,et al. Verifying Nonlinear Real Formulas Via Sums of Squares , 2007, TPHOLs.
[16] Benjamin Grégoire,et al. Extending Coq with Imperative Features and Its Application to SAT Verification , 2010, ITP.
[17] Assalé Adjé,et al. Property-based Polynomial Invariant Generation Using Sums-of-Squares Optimization , 2015, SAS.
[18] Stephen P. Boyd,et al. Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.
[19] James Demmel,et al. IEEE Standard for Floating-Point Arithmetic , 2008 .
[20] Benjamin Grégoire,et al. Full Reduction at Full Throttle , 2011, CPP.
[21] A. Tarski. A Decision Method for Elementary Algebra and Geometry , 2023 .
[22] Johan Löfberg,et al. Pre- and Post-Processing Sum-of-Squares Programs in Practice , 2009, IEEE Transactions on Automatic Control.
[23] Enrico Tassi,et al. A Small Scale Reflection Extension for the Coq system , 2008 .
[24] Jean B. Lasserre,et al. Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..
[25] Christine Paulin-Mohring,et al. The coq proof assistant reference manual , 2000 .
[26] Guillaume Melquiond,et al. Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq , 2011, 2011 IEEE 20th Symposium on Computer Arithmetic.
[27] Pablo A. Parrilo,et al. Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..
[28] George E. Collins,et al. Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .
[29] Victor Magron,et al. NLCertify: A Tool for Formal Nonlinear Optimization , 2014, ICMS.
[30] Sriram Sankaranarayanan,et al. Validating numerical semidefinite programming solvers for polynomial invariants , 2016, SAS.
[31] B. Borchers. CSDP, A C library for semidefinite programming , 1999 .
[32] Guillaume Melquiond,et al. Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq , 2016, Journal of Automated Reasoning.
[33] Yinyu Ye,et al. Algorithm 875: DSDP5—software for semidefinite programming , 2008, TOMS.
[34] Pierre Roux. Formal Proofs of Rounding Error Bounds With application to an automatic positive definiteness check , 2017 .
[35] Siegfried M. Rump,et al. Verification of Positive Definiteness , 2006 .