The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
Semidefinite Programming for Min-Max Problems and Games
[article]
2009
arXiv
pre-print
Preserved Fulltext
Other Versions
This provides a unified approach and a class of algorithms to approximate all Nash equilibria and min-max strategies of many static and dynamic games. ...
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum ...
Let P be the min-max problem defined in (3.2) . Let λ * d be the optimal value of the semidefinite program (5.9), and suppose that with r := max j=1,... ...
arXiv:0810.3150v2
fatcat:qwenkmtwbfanfosr75fqgmfbi4
Semidefinite programming for min–max problems and games
2010
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 2017; you can also visit the original URL.
The file type is application/pdf.
Key words and phrases. N -player games; Nash equlibria; min-max optimization problems; semidefinite programming. We would like to thank Bernhard von Stengel and the referees for their comments. ...
We consider two min-max problems: (1) minimizing the supremum of finitely many rational functions over a compact basic semi-algebraic set and (2) solving a 2-player zero-sum polynomial game in randomized ...
Let P be the min-max problem defined in (3.2) . Let λ * d be the optimal value of the semidefinite program (5.9) , and suppose that with r := max j=1,... ...
doi:10.1007/s10107-010-0353-y
fatcat:skzmuaws35ahhctyxzsv7jxr5q
Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming
[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.
Recently, a correspondence has been established between nonarchimedean semidefinite programs and stochastic mean payoff games with perfect information. ...
Nonarchimedean semidefinite programs encode parametric families of classical semidefinite programs, for sufficiently large values of the parameter. ...
Acknowledgement The second author thanks Vladimir Gurvich for enlightening discussions on the pumping algorithm of [GKK88] and its extension to stochastic games in [BEGM15] . ...
arXiv:1802.07712v1
fatcat:qypn46dt6vhdfdtxzqrtictitu
Parallel Approximation of Non-interactive Zero-sum Quantum Games
2009
2009 24th Annual IEEE Conference on Computational Complexity
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 2011; you can also visit the original URL.
The file type is application/pdf.
We prove that an equilibrium point of any such game can be approximated by means of an efficient parallel algorithm, which implies that one-turn quantum refereed games, wherein the referee is specified ...
This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to ...
We therefore thank Rohit Khandekar for his implicit and indirect contribution to this work, and for allowing us to include it in this paper. ...
doi:10.1109/ccc.2009.26
dblp:conf/coco/JainW09
fatcat:qsani3o7tfc5bolt5tjlwrbn3e
Parallel approximation of non-interactive zero-sum quantum games
[article]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We prove that an equilibrium point of any such game can be approximated by means of an efficient parallel algorithm, which implies that one-turn quantum refereed games, wherein the referee is specified ...
This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to ...
We therefore thank Rohit Khandekar for his implicit and indirect contribution to this work, and for allowing us to include it in this paper. ...
arXiv:0808.2775v1
fatcat:mekzd65ykrfmhk7apdc2anpepa
Solving generic nonarchimedean semidefinite programs using stochastic game algorithms
2018
Journal of symbolic computation
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:
2016 pre-print arXiv:1603.06916v2 fatcat:5w7ycleqrbf7xjngxqbdtf3yliOther Versions
This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances. ...
A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. ...
Acknowledgments We thank the referees for their detailed comments.
References ...
doi:10.1016/j.jsc.2017.07.002
fatcat:qvmjhlcyl5fb5pdqsgr3ya4dyi
A Spectral Generalization of Von Neumann Minimax Theorem
[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 2019; you can also visit the original URL.
The file type is application/pdf.
For diagonal A_i's this reduces to the classic minimax. ...
., A_m, the following spectral minimax property holds: min_X ∈Δ_nmax_y ∈ S_m∑_i=1^m y_iA_i ∙ X=max_y ∈ S_mmin_X ∈Δ_n∑_i=1^m y_iA_i ∙ X, where S_m is the simplex and Δ_n the spectraplex. ...
Furthermore, it is well known that in semidefinite programming, as a conic linear programming, if there exists a feasible X ≻ 0 and feasible (y, S) with S ≻ 0, the optimal objective value of both problems ...
arXiv:1905.09762v1
fatcat:y4d76ng7oram5avjuydkozvu3m
Polynomial games and sum of squares optimization
2006
Proceedings of the 45th IEEE Conference on Decision and Control
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.
We show that the value of the game, and the corresponding optimal strategies, can be obtained by solving a single semidefinite programming problem. ...
We study two-person zero-sum games, where the payoff function is a polynomial expression in the actions of the players. This class of games was introduced by Dresher, Karlin, and Shapley in 1950. ...
Alexandre Megretski, for his help with the translation of [20] , and to Noah Stein, for bringing Karlin's quote in Section II-B to my attention. ...
doi:10.1109/cdc.2006.377261
dblp:conf/cdc/Parrilo06
fatcat:nyitmlx4l5ewbnw2rchk2o2g3m
On Khot's unique games conjecture
2012
Bulletin of the American Mathematical Society
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 conjecture has inspired a remarkable body of work, which has clarified the computational complexity of several optimization problems and the effectiveness of "semidefinite programming" convex relaxations ...
In 2002, Subhash Khot formulated the Unique Games Conjecture, a conjecture about the computational complexity of certain optimization problems. ...
Semidefinite Programming and Unique Games. ...
doi:10.1090/s0273-0979-2011-01361-1
fatcat:olwc5dausved3fhbgb5fn6rx5y
A Direct Product Theorem for Discrepancy
2008
2008 23rd Annual IEEE Conference on Computational Complexity
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 2016; you can also visit the original URL.
The file type is application/pdf.
The main tool for our results is semidefinite programming, in particular a recent characterization of discrepancy in terms of a semidefinite programming quantity by Linial and Shraibman (2006) . ...
As a consequence we obtain a strong direct product theorem for distributional complexity, and direct sum theorems for worst-case complexity, for bounds shown by the discrepancy method. ...
A (now) common approach for dealing with NP-hard problems is to consider a semidefinite relaxation of the problem. ...
doi:10.1109/ccc.2008.25
dblp:conf/coco/LeeSS08
fatcat:o2ugisl5ejddxhejo2ztg6vcry
Multireference alignment using semidefinite programming
2014
Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14
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.
Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment ...
Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical ...
Acknowledgements The authors thank Yutong Chen for valuable assistance with the implementation of our algorithm. A. S. Bandeira was supported by AFOSR Grant No. FA9550-12-1-0317. M. ...
doi:10.1145/2554797.2554839
dblp:conf/innovations/BandeiraCSZ14
fatcat:5nl2fjexbvgk3h3wemz4lrixea
A Semidefinite Hierarchy for Disjointly Constrained Multilinear Programming
[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.
For nondegenerate bimatrix games, a Nash equilibrium can be computed by the sum of squares approach in finitely many steps. ...
Based on a reformulation of the problem in terms of sum-of-squares polynomials, we study a hierarchy of semidefinite relaxations to the problem. ...
The multilinear problem (1.1) can equivalently be stated as a nonnegativity question f * = max {f (x 1 , . . . , x l ) | x i ∈ P i , i ∈ [l]} = min {µ | µ − f (x 1 , . . . , x l ) ≥ 0 for (x 1 , . . . ...
arXiv:1603.03634v1
fatcat:happcknkmzacfbb4q2c774zxky
In SDP relaxations, inaccurate solvers do robust optimization
[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:
2019 pre-print arXiv:1811.02879v2 fatcat:y3pie54fwnhvne5pxywy4vkuteOther Versions
In other words the resulting procedure can be viewed as a 'max-min' robust optimization problem with two players (the solver which maximizes on B_∞(f,ε) and the user who minimizes over the original decision ...
We interpret some wrong results (due to numerical inaccuracies) already observed when solving SDP-relaxations for polynomial optimization on a double precision floating point SDP solver. ...
But in fact, as we are in the convex case, Theorem 2.1 implies that this max − min game is also equivalent to the min − max game. ...
arXiv:1811.02879v3
fatcat:4oz6nbfhnbfqtbrrf4vsa3m6d4
Product theorems via semidefinite programming
[article]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
classes of games. ...
The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovasz to determine the Shannon capacity of the pentagon; to ...
Acknowledgements We would like to thank Mario Szegedy for many insightful conversations. We would also like to thank the anonymous referees of ICALP 2008 for their helpful comments. ...
arXiv:0803.4206v2
fatcat:oyfcxdqfvnca5fny2nsic6t5ay
Product Theorems Via Semidefinite Programming
[chapter]
2008
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 2017; you can also visit the original URL.
The file type is application/pdf.
classes of games. ...
The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovász to determine the Shannon capacity of the pentagon; to ...
Acknowledgements We would like to thank Mario Szegedy for many insightful conversations. We would also like to thank the anonymous referees of ICALP 2008 for their helpful comments. ...
doi:10.1007/978-3-540-70575-8_55
fatcat:a4o4vabbw5aqrageattra5lm2m
« Previous
Showing results 1 — 15 out of 2,835 results