A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Filters
Sum-of-squares hierarchy lower bounds for symmetric formulations
[article]
2016
arXiv
pre-print
Preserved Fulltext
Other Versions
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. ...
More precisely, we give a short elementary proof of Grigoriev/Laurent lower bound for finding the integer cut polytope of the complete graph. ...
The authors would like to express their gratitude to Ola Svensson for helpful discussions and ideas regarding this paper. ...
arXiv:1407.1746v2
fatcat:wxu7jef6gvc2nk3iq4kh3pukhq
On the Power of Symmetric LP and SDP Relaxations
2014
2014 IEEE 29th Conference on Computational Complexity (CCC)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
This result gives the first lower bounds for symmetric SDP relaxations of Max CSPs, and indicates that the sum-of-squares method provides the "right" SDP relaxation for this class of problems. ...
Concretely, for k < n/4, we show that k-rounds of sum-ofsquares / Lasserre relaxations of size k n k achieve best-possible approximation guarantees for Max CSPs among all symmetric SDP relaxations of size ...
Combined with known lower bounds for sum-of-squares relaxations [17] - [19] , this result implies the first explicit lower bounds for general symmetric SDP relaxations of natural optimization problems ...
doi:10.1109/ccc.2014.10
dblp:conf/coco/LeeRST14
fatcat:rljvsqsehvfmvnnjoz6wrtidhq
Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies
2015
SIAM Journal on Optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We use this framework to study two well-known families of polytopes, namely the parity polytope and the cut polytope, and we prove exponential lower bounds for equivariant psd lifts of these polytopes. ...
Our main result is a structure theorem where we show that any equivariant psd lift of size d of an orbitope is of sum-of-squares type where the functions in the sum-of-squares decomposition come from an ...
The authors would like to thank the anonymous referees for their thorough comments which helped improve the paper, in particular Theorem 1.6. ...
doi:10.1137/140966265
fatcat:vrjpdsih7bhonjslfwpjbwpe7a
From combinatorial optimization to real algebraic geometry and back
2014
Croatian Operational Research Review
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-field of real algebraic geometry. ...
We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. ...
We can use a result, first formulated in [39] , that characterizes the monomials that can appear in a sum of squares representation. ...
doi:10.17535/crorr.2014.0001
fatcat:fngmhkpzyza5jjhe4ssc7k5st4
On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. ...
More precisely, we show that any inner approximation to the cone of positive homogeneous polynomials that is arbitrarily tight can be turned into a converging hierarchy of lower bounds for general polynomial ...
We are grateful to Pablo Parrilo for very insightful comments, particularly as regards Section 4 and the observation that any form can be made even by only doubling the number of variables and the degree ...
arXiv:1709.09307v2
fatcat:bnks6dbefjb7hmatquefb2dy2q
Tight Sum-of-Squares lower bounds for binary polynomial optimization problems
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We give two results concerning the power of the Sum-of-Squares(SoS)/Lasserre hierarchy. ...
We disprove this conjecture and derive lower and upper bounds for the rank. ...
The authors would like to express their gratitude to Alessio Benavoli for helpful discussions. ...
arXiv:1605.03019v1
fatcat:fa4fy753kndgvlk6pals7jjspq
Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
This formulation is subsequently solved using the Lasserre moment-sum-of-squares hierarchy, generating a sequence of outer convex approximations that monotonically converges from below to the optimum of ...
These theoretical findings are illustrated on several examples of topology optimization of frames and shells, for which we observe that the hierarchy converges in a finite (rather small) number of steps ...
Acknowledgements We thank Edita Dvořáková for providing us with her implementation of the MITC4 shell elements (Dvořáková, 2015) . ...
arXiv:2009.12560v1
fatcat:fosmdfwht5eyratttcahd5mvsy
Query complexity in expectation
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We exactly characterize both the randomized and the quantum query complexity by two polynomial degrees, the nonnegative literal degree and the sum-of-squares degree, respectively. ...
Since query complexity can be used to upper bound communication complexity of related functions, we can derive some upper bounds on psd extension complexity by constructing efficient quantum query algorithms ...
us a version of [LRS14] . ...
arXiv:1411.7280v1
fatcat:qqpeu43kjnejfg5ipo24zxdkze
Geometry of 3D Environments and Sum of Squares Polynomials
2017
Robotics: Science and Systems XIII
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We use algebraic techniques from sum of squares optimization that reduce all these tasks to semidefinite programs of small size and present numerical experiments in realistic scenarios. ...
Fig. 1 : Sublevel sets of sos-convex polynomials of increasing degree (left); sublevel sets of sos polynomials of increasing nonconvexity (middle); growth and shrinkage of an sos-body with sublevel sets ...
ACKNOWLEDGEMENTS We thank Erwin Coumans, Mrinal Kalakrishnan and Vincent Vanhoucke for several technically insightful discussions and guidance. ...
doi:10.15607/rss.2017.xiii.071
dblp:conf/rss/AhmadiHMS17
fatcat:qcefmbj4lveqdjqbnmlouijz54
Query Complexity in Expectation
[chapter]
2015
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
Since query complexity can be used to upper bound communication complexity of related functions, we can derive some upper bounds on psd extension complexity by constructing efficient quantum query algorithms ...
We observe that the quantum complexity can be unboundedly smaller than the classical complexity for some functions, but can be at most polynomially smaller for functions with range {0, 1}. ...
us a version of [LRS14] . ...
doi:10.1007/978-3-662-47672-7_62
fatcat:a6fesbjv45fi3ehtxfmewvcj24
Geometry of 3D Environments and Sum of Squares Polynomials
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We use algebraic techniques from sum of squares optimization that reduce all these tasks to semidefinite programs of small size and present numerical experiments in realistic scenarios. ...
of two convex basic semalgebraic sets that overlap, and tight containment of the union of several basic semialgebraic sets with a single convex one. ...
ACKNOWLEDGEMENTS We thank Erwin Coumans, Mrinal Kalakrishnan and Vincent Vanhoucke for several technically insightful discussions and guidance. ...
arXiv:1611.07369v3
fatcat:vzscnfcylfafdf444vmxdpaspq
Semidefinite Programming and Nash Equilibria in Bimatrix Games
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2018 pre-print arXiv:1706.08550v2 fatcat:2rf3vs7eina45pao5gpmvr7vwmOther Versions
Finally, we show the connection between our SDP and the first level of the Lasserre/sum of squares hierarchy. ...
We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem and provide a number of valid inequalities to improve the quality of the relaxation. ...
We would like to thank Ilan Adler, Costis Daskalakis, Georgina Hall, Ramon van Handel, and Robert Vanderbei for insightful exchanges. ...
arXiv:1706.08550v3
fatcat:5zwr6lcukbhu3m3fvv54zba2ri
A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem
2017
Annals of Operations Research
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre et al. ...
(EURO J Comput Optim 1-31, 2015) constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. ...
Acknowledgements The authors would like to thank Claudia D'Ambrosio and Ruth Misener for useful discussions and providing us some references. ...
doi:10.1007/s10479-017-2407-5
fatcat:em25wdtc5jh5pjcurxafbrzj5u
The sum-of-squares hierarchy on the sphere and applications in quantum information theory
2020
Mathematical programming
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. ...
By exploiting the duality relation between sums of squares and the Doherty-Parrilo-Spedalieri hierarchy in quantum information theory, we show that our result generalizes to nonquadratic polynomials the ...
We will actually prove a more general result giving bounds on the performance of the sum-of-squares hierarchy for all values of the level . ...
doi:10.1007/s10107-020-01537-7
fatcat:dvmmitjc7veifescq5t3pdbn6e
The matching problem has no small symmetric SDP
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We answer this question negatively for symmetric SDPs: any symmetric SDP for the matching problem has exponential size. ...
We also show that an O(k)-round Lasserre SDP relaxation for the metric traveling salesperson problem yields at least as good an approximation as any symmetric SDP relaxation of size n^k. ...
We now turn a G-coordinate-symmetric SDP formulation into a symmetric sum of squares representation over a small set of basis functions.
Lemma 2.3 (Sum of squares for a symmetric SDP formulation). ...
arXiv:1504.00703v5
fatcat:vddxee5knjeehp3nlhgvzrt5ia
« Previous
Showing results 1 — 15 out of 18,656 results