Fetching the paper…
Reading the bibliography…
We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program.
S. A. Gershgorin, Uber die Abgrenzung der Eigenwerte einer Matrix , Bulletin de l’Académie des Sciences de l’URSS. Classe des sciences mathématiques et na (1931), no. 6, 749–754
1931
Earlier work this paper cites.
T. S. Motzkin, The arithmetic-geometric inequality , Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 205–224. MR MR0223521 (36 #6569)
1967
Earlier work this paper cites.
R. M. Karp, Reducibility among combinatorial problems , Springer, 1972
1972
Earlier work this paper cites.
G. Barker and D. Carlson, Cones of diagonally dominant matrices , Pacific Journal of Mathematics 57
1975
Earlier work this paper cites.
L. Lovász, On the Shannon capacity of a graph , IEEE Transactions on Information Theory 25
1979
Earlier work this paper cites.
B. Reznick, Uniform denominators in Hilbert’s 17th problem , Math Z. 220
1995
Earlier work this paper cites.
J. A. de Loera and F. Santos, An effective version of pólya’s theorem on positive definite forms , Journal of Pure and Applied Algebra 108
1996
Earlier work this paper cites.
L. Vandenberghe and S. Boyd, Semidefinite programming , SIAM Review 38
1996
Earlier work this paper cites.
M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, Applications of second-order cone programming , Linear algebra and its applications 284
1998
Earlier work this paper cites.
Y. Nesterov, Squared functional systems and optimization problems , High performance optimization, Appl. Optim., vol. 33, Kluwer Acad. Publ., Dordrecht, 2000, pp. 405–440
2000
Earlier work this paper cites.
P. A. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , Ph.D. thesis, California Institute of Technology, May 2000
2000
Earlier work this paper cites.
by same author, Some concrete aspects of Hilbert’s 17th problem , Contemporary Mathematics, vol. 253, American Mathematical Society, 2000, pp. 251–272
2000
Earlier work this paper cites.
J. B. Lasserre, Global optimization with polynomials and the problem of moments , SIAM Journal on Optimization 11
2001
Cited alongside, same era.
M. R. Garey and D. S. Johnson, Computers and Intractability , vol. 29, Wh Freeman, 2002
2002
Cited alongside, same era.
F. Alizadeh and D. Goldfarb, Second-order cone programming , Mathematical programming 95
2003
Cited alongside, same era.
by same author, Semidefinite programming relaxations for semialgebraic problems , Mathematical Programming 96
2003
Cited alongside, same era.
P. A. Parrilo and B. Sturmfels, Minimizing polynomial functions , Algorithmic and Quantitative Real Algebraic Geometry, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 60
2003
Cited alongside, same era.
A. A. Ahmadi, Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis , Ph.D. thesis, Massachusetts Institute of Technology, September 2011, Available at http://aaa.princeton.edu/publications
2011
Later among the works it cites.
P. J. C. Dickinson and L. Gijben, On the computational complexity of membership problems for the completely positive cone and its dual , Available at http://www.optimization-online.org/DB-FILE/2011/05/3041.pdf
2011
Later among the works it cites.
Gurobi optimizer reference manual , URL: http://www. gurobi. com (2012)
2012
Later among the works it cites.
M. Laurent and F. Vallentin, Lecture Notes on Semidefinite Optimization , 2012
2012
Later among the works it cites.
MOSEK reference manual , 2013, Version 7. Latest version available at http://www.mosek.com/
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
S. Boyd and L. Vandenberghe, Convex Optimization , Cambridge University Press, 2004
2004
Cited alongside, same era.
J. Löfberg, Yalmip : A toolbox for modeling and optimization in MATLAB , Proceedings of the CACSD Conference, 2004, Available from http://control.ee.ethz.ch/
2004
Cited alongside, same era.
M. C. Golumbic, Algorithmic graph theory and its applications , Graph Theory, Combinatorics and Algorithms, Springer, 2005, pp. 41–62
2005
Cited alongside, same era.
D. Henrion and A. Garulli (eds.), Positive polynomials in control , Lecture Notes in Control and Information Sciences, vol. 312, Springer, 2005
2005
Cited alongside, same era.
N. Gvozdenović and M. Laurent, Semidefinite bounds for the stability number of a graph via sums of squares of polynomials , Mathematical Programming 110
2007
Cited alongside, same era.
M. Laurent, Sums of squares, moment matrices and optimization over polynomials , Emerging applications of algebraic geometry, Springer, 2009, pp. 157–270
2009
Cited alongside, same era.
CPLEX, V12. 4: Users manual for CPLEX , International Business Machines Corporation 46
Cited in the paper.
A. Megretski, SPOT: systems polynomial optimization tools , 2013
2013
Later among the works it cites.
A. A. Ahmadi and A. Majumdar, DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization , Proceedings of the 48th Annual Conference on Information Sciences and Systems, Princeton University, 2014
2014
Later among the works it cites.
A. Majumdar, A. A. Ahmadi, and R. Tedrake, Control and verification of high-dimensional systems via DSOS and SDSOS optimization , Proceedings of the 53 rd
2014
Later among the works it cites.
A. A. Ahmadi, S. Dash, and G. Hall, Optimization over structured subsets of positive semidefinite matrices via column generation , Under Review, 2015
2015
Closest in time.
by same author, DSOS and SDSOS: more tractable alternatives to sum of squares and semidefinite optimization , In preparation, 2015
2015
Closest in time.