(no subject)
Putinar's Positivstellensatz
and Lasserre's relaxation.
Parrilo P.A. (2000) "Structured semidefinite
programs and semialgebraic geometry methods in
robustness and optimization." PhD thesis (California
Institute of Technology, Pasadena, CA).
Parrilo P.A. (2003) "Semidefinite programming
relaxations for semialgebraic problems."
Mathematical Programming 96(2):293-320.
Lasserre J.-B. (2001) "Global optimization with
polynomials and the problem of moments."
SIAM J. Optim. 11:796-817.
J. B. Lasserre (2002) "Polynomials nonnegative
on a grid and discrete optimization"
Trans. Amer. Math. Soc., 354, pp. 631-649.
J. B. Lasserre (2002) "Semidefinite programming
vs. LP relaxations for polynomial programming"
Math. Oper. Res., 27, pp. 347-360.
D. Henrion, J. B. Lasserre (2003) "GloptiPoly:
Global optimization over polynomials with Matlab and SeDuMi"
ACM Trans. Math. Software, 29, pp. 165-194.
http://homepages.laas.fr/henrion/software/gloptipoly2/
J. B. Lasserre (2004) "Polynomial programming:
LP-relaxations also converge"
SIAM J. Optim., 15, pp. 383-393.
J. B. Lasserre (2005) "Sum of squares approximation
of polynomials, nonnegative on a real algebraic set"
SIAM J. Optim., 16, pp. 610-628.
Lasserre J.B. (2005) "IP, duality and superadditive
functions" Contemporary Mathematics 374, 139-150.
J. B. Lasserre (2006) "Convergent SDP-relaxations
in polynomial optimization with sparsity"
SIAM J. Optim., 17, pp. 822-843.
Lasserre J.B., Prieto-Rumeau T., Zervos M. (2006)
"Pricing a class of exotic options via moments and
SDP relaxations," Math. Finance 16, 469-494.
Lasserre J.B. (2007) "A sum of squares approximation
of nonnegative polynomials" SIAM Review 49, 651-669.
Lasserre J.B., Laurent M., Rostalski P. (2007)
"Semidefinite characterization and computation of zero-
dimensional real radical ideals" Found. Comp. Math. 8, 607-647.
J.W. Hilton, J.-B. Lasserre, M.Putinar (2008)
"Measures with zeros in the inverse of their moment matrix"
The Annals of Probab., Vol.36(4), 1453-1471.
J.-B. Lasserre (2008) "Representation
of nonnegative convex polynomials".
J.-B. Lasserre (2008) "Convexity in semi-algebraic
geometry and polynomial optimization".
J. Nie, M. Schweighofer (2008)
"On the complexity of Putinar's Positivstellensatz"
Lasserre, J.B. (2009) "Convex sets with semidefinite
representation" Math. Prog. 120, 457-477.
D. Henrion, J.B. Lasserre, J. Lofberg (2009) "GloptiPoly 3:
moments, optimization and semidefinite programming",
Optim. Methods and Software, Vol.24, Nos.4-5, pp.761-779.
J.-B. Lasserre, S. Zeron (2009) "Certificates
and relaxations for integer programming and
the semi-group membership problem".
J.-B. Lasserre (2009) "Certificates of
convexity for basic semi-algebraic sets".
J.-B. Lasserre, M. Putinar (2009) "Positivity
and optimization for semi-algebraic functions".
Lasserre J.B. (2011) "A new look at nonnegativity
on closed sets and polynomial optimization."
SIAM J. Optim. 21, 864-885.
Lasserre J.B. (2011) "Bounding the support of a measure from
its marginal moments," Proc. Amer. Math. Soc. 139, 3375-3382.
D. Henrion, J.-B. Lasserre, M. Mevissen (2012) "Mean
squared error minimization for inverse moment problems".
J.-B. Lasserre (2012) "A Lagrangian relaxation
view of linear and semidefinite hierarchies".
Laraki R., Lasserre J.B. (2012) "SDP for min-max problems
and games," Math. Program. Ser. A 131, 305-332.
Lasserre J.B. (2013) "Recovering an homogeneous
polynomial from moments of its level set,"
Discrete & Comp. Geom. 50, pp. 673-678.
J.-B. Lasserre, M. Putinar (2014) "Reconstruction
of algebraic-exponential data from moments".
E. Pauwels, D. Henrion, J.-B. Lasserre (2014)
"Inverse optimal control with polynomial optimization"
D. Henrion, E. Pauwels (2014) "Linear conic
optimization for nonlinear optimal control".
J. Bolte, E. Pauwels (2015) "Majorization-minimization
procedures and convergence of SQP methods for
semi-algebraic and tame programs."
E. Pauwels, D. Henrion, J.-B. Lasserre (2015)
"Linear conic optimization for inverse optimal control".
J.-B. Lasserre, T. Kim-Chuan, Y. Shouguang (2015)
"A bounded degree SOS hierarchy for polynomial optimization".
J.-B. Lasserre (2015) "Lebesgue decomposition
in action via semidefinite relaxations".
Y. De Castro, F. Gamboa, D. Henrion, J.-B. Lasserre (2015)
"Exact solutions to Super Resolution on semi-algebraic
domains in higher dimensions".
Lasserre J.B., Putinar M. (2015)
"Algebraic-exponential Data Recovery from Moments"
Discrete & Comput. Geom. 54, pp. 993-1012.
Magron V., Henrion D., Lasserre J.B. (2015)
"Semidefinite approximations of projections
and polynomial images of semi-algebraic sets"
SIAM J. Optim. 25, pp. 2143-2164.
J.-B. Lasserre (2015) "A max-cut
formulation of 0/1 programs".
(Before that J.B. Lasserre also
worked on Barvinok's algorithm).
Books:
J.-B. Lasserre (2015) "An Introduction to Polynomial and
Semi-Algebraic Optimization," Cambridge University Press,
Cambridge, 2015. ISBN: 9781107630697.
R. Cominetti, F. Facchinei, J.B. Lasserre (2012) "Modern
Optimization Modelling Techniques" Birkhauser Verlag, Berlin.
J.-B. Lasserre (2009) "Moments, Positive Polynomials and
Their Applications" Imper.College Press, Optimiz. Ser.).
Jiawang Nie: MATH 271C course,
Spring 2010. @math.ucsd.edu
C.f. (for upcoming applications):
B. Barak, J.A. Kelner, D. Steurer (2015)
"Rounding Sum-of-Squares Relaxations".
B. Barak, F.G.S.L. Brandao, A.W. Harrow, J. Kelner,
D. Steurer, Y. Zhou (2014) "Hypercontractivity,
Sum-of-Squares Proofs, and their Applications".
S. Hopkins, J. Shi, D. Steurer (2015) "Tensor PCA via
sum-of-squares proofs" JMLR: WS and Conf. Proc., vol.40:1-51.
S. Benabbas, S.O. Chan, K. Georgiou, A. Magen (2011)
"Tight Gaps for Vertex Cover in the Sherali-Adams SDP Hierarchy".
V. Chandrasekaran , M.I. Jordan (2012) "Computational
and Statistical Tradeoffs via Convex Relaxation".
M.Pilanci, M.J. Wainwright, L. El Ghaoui (2015)
"Sparse learning via Boolean relaxations".
Wainwright, M.J., Jordan, M.I. (2004)
"Treewidth-based conditions for exactness
of the Sherali-Adams and Lasserre relaxations."
Techn. rep., UC Berkeley, Dept. of Stat., No.671.
and Lasserre's relaxation.
Parrilo P.A. (2000) "Structured semidefinite
programs and semialgebraic geometry methods in
robustness and optimization." PhD thesis (California
Institute of Technology, Pasadena, CA).
Parrilo P.A. (2003) "Semidefinite programming
relaxations for semialgebraic problems."
Mathematical Programming 96(2):293-320.
Lasserre J.-B. (2001) "Global optimization with
polynomials and the problem of moments."
SIAM J. Optim. 11:796-817.
J. B. Lasserre (2002) "Polynomials nonnegative
on a grid and discrete optimization"
Trans. Amer. Math. Soc., 354, pp. 631-649.
J. B. Lasserre (2002) "Semidefinite programming
vs. LP relaxations for polynomial programming"
Math. Oper. Res., 27, pp. 347-360.
D. Henrion, J. B. Lasserre (2003) "GloptiPoly:
Global optimization over polynomials with Matlab and SeDuMi"
ACM Trans. Math. Software, 29, pp. 165-194.
http://homepages.laas.fr/henrion/software/gloptipoly2/
J. B. Lasserre (2004) "Polynomial programming:
LP-relaxations also converge"
SIAM J. Optim., 15, pp. 383-393.
J. B. Lasserre (2005) "Sum of squares approximation
of polynomials, nonnegative on a real algebraic set"
SIAM J. Optim., 16, pp. 610-628.
Lasserre J.B. (2005) "IP, duality and superadditive
functions" Contemporary Mathematics 374, 139-150.
J. B. Lasserre (2006) "Convergent SDP-relaxations
in polynomial optimization with sparsity"
SIAM J. Optim., 17, pp. 822-843.
Lasserre J.B., Prieto-Rumeau T., Zervos M. (2006)
"Pricing a class of exotic options via moments and
SDP relaxations," Math. Finance 16, 469-494.
Lasserre J.B. (2007) "A sum of squares approximation
of nonnegative polynomials" SIAM Review 49, 651-669.
Lasserre J.B., Laurent M., Rostalski P. (2007)
"Semidefinite characterization and computation of zero-
dimensional real radical ideals" Found. Comp. Math. 8, 607-647.
J.W. Hilton, J.-B. Lasserre, M.Putinar (2008)
"Measures with zeros in the inverse of their moment matrix"
The Annals of Probab., Vol.36(4), 1453-1471.
J.-B. Lasserre (2008) "Representation
of nonnegative convex polynomials".
J.-B. Lasserre (2008) "Convexity in semi-algebraic
geometry and polynomial optimization".
J. Nie, M. Schweighofer (2008)
"On the complexity of Putinar's Positivstellensatz"
Lasserre, J.B. (2009) "Convex sets with semidefinite
representation" Math. Prog. 120, 457-477.
D. Henrion, J.B. Lasserre, J. Lofberg (2009) "GloptiPoly 3:
moments, optimization and semidefinite programming",
Optim. Methods and Software, Vol.24, Nos.4-5, pp.761-779.
J.-B. Lasserre, S. Zeron (2009) "Certificates
and relaxations for integer programming and
the semi-group membership problem".
J.-B. Lasserre (2009) "Certificates of
convexity for basic semi-algebraic sets".
J.-B. Lasserre, M. Putinar (2009) "Positivity
and optimization for semi-algebraic functions".
Lasserre J.B. (2011) "A new look at nonnegativity
on closed sets and polynomial optimization."
SIAM J. Optim. 21, 864-885.
Lasserre J.B. (2011) "Bounding the support of a measure from
its marginal moments," Proc. Amer. Math. Soc. 139, 3375-3382.
D. Henrion, J.-B. Lasserre, M. Mevissen (2012) "Mean
squared error minimization for inverse moment problems".
J.-B. Lasserre (2012) "A Lagrangian relaxation
view of linear and semidefinite hierarchies".
Laraki R., Lasserre J.B. (2012) "SDP for min-max problems
and games," Math. Program. Ser. A 131, 305-332.
Lasserre J.B. (2013) "Recovering an homogeneous
polynomial from moments of its level set,"
Discrete & Comp. Geom. 50, pp. 673-678.
J.-B. Lasserre, M. Putinar (2014) "Reconstruction
of algebraic-exponential data from moments".
E. Pauwels, D. Henrion, J.-B. Lasserre (2014)
"Inverse optimal control with polynomial optimization"
D. Henrion, E. Pauwels (2014) "Linear conic
optimization for nonlinear optimal control".
J. Bolte, E. Pauwels (2015) "Majorization-minimization
procedures and convergence of SQP methods for
semi-algebraic and tame programs."
E. Pauwels, D. Henrion, J.-B. Lasserre (2015)
"Linear conic optimization for inverse optimal control".
J.-B. Lasserre, T. Kim-Chuan, Y. Shouguang (2015)
"A bounded degree SOS hierarchy for polynomial optimization".
J.-B. Lasserre (2015) "Lebesgue decomposition
in action via semidefinite relaxations".
Y. De Castro, F. Gamboa, D. Henrion, J.-B. Lasserre (2015)
"Exact solutions to Super Resolution on semi-algebraic
domains in higher dimensions".
Lasserre J.B., Putinar M. (2015)
"Algebraic-exponential Data Recovery from Moments"
Discrete & Comput. Geom. 54, pp. 993-1012.
Magron V., Henrion D., Lasserre J.B. (2015)
"Semidefinite approximations of projections
and polynomial images of semi-algebraic sets"
SIAM J. Optim. 25, pp. 2143-2164.
J.-B. Lasserre (2015) "A max-cut
formulation of 0/1 programs".
(Before that J.B. Lasserre also
worked on Barvinok's algorithm).
Books:
J.-B. Lasserre (2015) "An Introduction to Polynomial and
Semi-Algebraic Optimization," Cambridge University Press,
Cambridge, 2015. ISBN: 9781107630697.
R. Cominetti, F. Facchinei, J.B. Lasserre (2012) "Modern
Optimization Modelling Techniques" Birkhauser Verlag, Berlin.
J.-B. Lasserre (2009) "Moments, Positive Polynomials and
Their Applications" Imper.College Press, Optimiz. Ser.).
Jiawang Nie: MATH 271C course,
Spring 2010. @math.ucsd.edu
C.f. (for upcoming applications):
B. Barak, J.A. Kelner, D. Steurer (2015)
"Rounding Sum-of-Squares Relaxations".
B. Barak, F.G.S.L. Brandao, A.W. Harrow, J. Kelner,
D. Steurer, Y. Zhou (2014) "Hypercontractivity,
Sum-of-Squares Proofs, and their Applications".
S. Hopkins, J. Shi, D. Steurer (2015) "Tensor PCA via
sum-of-squares proofs" JMLR: WS and Conf. Proc., vol.40:1-51.
S. Benabbas, S.O. Chan, K. Georgiou, A. Magen (2011)
"Tight Gaps for Vertex Cover in the Sherali-Adams SDP Hierarchy".
V. Chandrasekaran , M.I. Jordan (2012) "Computational
and Statistical Tradeoffs via Convex Relaxation".
M.Pilanci, M.J. Wainwright, L. El Ghaoui (2015)
"Sparse learning via Boolean relaxations".
Wainwright, M.J., Jordan, M.I. (2004)
"Treewidth-based conditions for exactness
of the Sherali-Adams and Lasserre relaxations."
Techn. rep., UC Berkeley, Dept. of Stat., No.671.