Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions
暂无分享,去创建一个
[1] John B. Moore,et al. A finite steps algorithm for solving convex feasibility problems , 2007, J. Glob. Optim..
[2] Adrian S. Lewis,et al. HIFOO - A MATLAB package for fixed-order controller design and H ∞ optimization , 2006 .
[3] Willard Miller,et al. The IMA volumes in mathematics and its applications , 1986 .
[4] N. Higham. Computing the nearest correlation matrix—a problem from finance , 2002 .
[5] Aharon Ben-Tal,et al. Lectures on modern convex optimization , 1987 .
[6] Alexander Schrijver,et al. Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.
[7] Yurii Nesterov,et al. Smooth minimization of non-smooth functions , 2005, Math. Program..
[8] John B. Moore,et al. A Newton-like method for solving rank constrained linear matrix inequalities , 2006, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).
[9] J. Hiriart-Urruty,et al. Convex analysis and minimization algorithms , 1993 .
[10] D K Smith,et al. Numerical Optimization , 2001, J. Oper. Res. Soc..
[11] Mihai Putinar,et al. POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION , 2006 .
[12] Farid Alizadeh,et al. Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization , 1995, SIAM J. Optim..
[13] Yurii Nesterov,et al. Squared Functional Systems and Optimization Problems , 2000 .
[14] Didier Henrion,et al. GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi , 2003, TOMS.
[15] Stephen P. Boyd,et al. Linear Matrix Inequalities in Systems and Control Theory , 1994 .
[16] M. Todd,et al. Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems , 2005 .
[17] Henry Wolkowicz,et al. Strong duality and minimal representations for cone optimization , 2012, Computational Optimization and Applications.
[18] Hans D. Mittelmann,et al. An independent benchmarking of SDP and SOCP solvers , 2003, Math. Program..
[19] Jos F. Sturm,et al. A Matlab toolbox for optimization over symmetric cones , 1999 .
[20] Heinz H. Bauschke,et al. On the convergence of von Neumann's alternating projection algorithm for two sets , 1993 .
[21] Adrian S. Lewis,et al. Alternating Projections on Manifolds , 2008, Math. Oper. Res..
[22] Didier Henrion,et al. SDLS: a Matlab package for solving conic least-squares problems , 2007, 0709.2556.
[23] P. Parrilo. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .
[24] B. Reznick,et al. Sums of squares of real polynomials , 1995 .
[25] O. Taussky. Sums of Squares , 1970 .
[26] Henry Wolkowicz,et al. Handbook of Semidefinite Programming , 2000 .
[27] S. Sullivant,et al. Emerging applications of algebraic geometry , 2009 .
[28] B. Craven,et al. Generalizations of Farkas’ Theorem , 1977 .
[29] N. Higham. COMPUTING A NEAREST SYMMETRIC POSITIVE SEMIDEFINITE MATRIX , 1988 .
[30] 邵文革,et al. Gilbert综合征二例 , 2009 .
[31] Jérôme Malick,et al. A Dual Approach to Semidefinite Least-Squares Problems , 2004, SIAM J. Matrix Anal. Appl..
[32] Didier Henrion,et al. GloptiPoly 3: moments, optimization and semidefinite programming , 2007, Optim. Methods Softw..
[33] Pablo A. Parrilo,et al. Computing sum of squares decompositions with rational coefficients , 2008 .
[34] Stephen P. Boyd,et al. Least-Squares Covariance Matrix Adjustment , 2005, SIAM J. Matrix Anal. Appl..
[35] 丸山 徹. Convex Analysisの二,三の進展について , 1977 .
[36] Laurent El Ghaoui,et al. Rank Minimization under LMI constraints: A Framework for Output Feedback Problems , 2007 .
[37] E. Yaz. Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.
[38] Johan Löfberg,et al. Pre- and Post-Processing Sum-of-Squares Programs in Practice , 2009, IEEE Transactions on Automatic Control.
[39] B. Dumitrescu. Positive Trigonometric Polynomials and Signal Processing Applications , 2007 .
[40] F. Giannessi. Variational Analysis and Generalized Differentiation , 2006 .
[41] Jean B. Lasserre,et al. Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..
[42] R. Dykstra. An Algorithm for Restricted Least Squares Regression , 1983 .
[43] Franz Rendl,et al. An Augmented Primal-Dual Method for Linear Conic Programs , 2008, SIAM J. Optim..
[44] A. Ivic. Sums of squares , 2020, An Introduction to 𝑞-analysis.
[45] Stephen P. Boyd,et al. Further Relaxations of the SDP Approach to Sensor Network Localization , 2007 .
[46] Hilmar Drygas. On a generalization of the Farkas theorem , 1969 .
[47] Arkadi Nemirovski,et al. The projective method for solving linear matrix inequalities , 1997, Math. Program..
[48] V. Powers,et al. An algorithm for sums of squares of real polynomials , 1998 .
[49] Adrian S. Lewis,et al. Local Linear Convergence for Alternating and Averaged Nonconvex Projections , 2009, Found. Comput. Math..
[50] Hans Frenk,et al. High performance optimization , 2000 .
[51] M. Laurent. Sums of Squares, Moment Matrices and Optimization Over Polynomials , 2009 .
[52] Stephen P. Boyd,et al. Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.
[53] A. Garulli,et al. Positive Polynomials in Control , 2005 .
[54] Nicholas J. Higham,et al. A Preconditioned Newton Algorithm for the Nearest Correlation Matrix , 2010 .
[55] Defeng Sun,et al. Quadratic Convergence and Numerical Experiments of Newton ’ s Method for Computing the Nearest Correlation Matrix , 2005 .