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The complexity of approximating a nonlinear program

1995
*
Mathematical programming
*

We show that there is no

doi:10.1007/bf01585569
fatcat:jmegfrb7v5flpiquskl6r7o67a
*polynomial*time*approximation**algorithm*for this problem, even one with a very poor guarantee, unless P = NP. ... As with NP-hard problems in combinatorial optimization, interest is turning to the development of (efficient)*approximation**algorithms*-*algorithms*which run in*polynomial*time and find a solution not too ... We thank*an*anonymous referee for comments. ...##
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The Complexity of Approximating a Nonlinear Program
[chapter]

1993
*
Complexity in Numerical Optimization
*

We show that there is no

doi:10.1142/9789814354363_0002
fatcat:foxxtsqz35bfdcchech42f7bcm
*polynomial*time*approximation**algorithm*for this problem, even one with a very poor guarantee, unless P = NP. ... As with NP-hard problems in combinatorial optimization, interest is turning to the development of (efficient)*approximation**algorithms*-*algorithms*which run in*polynomial*time and find a solution not too ... We thank*an*anonymous referee for comments. ...##
###
Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs
[article]

2018
*
arXiv
*
pre-print

Our

arXiv:1806.11282v1
fatcat:cyuqsil4bbe2ffzcscupsis26a
*algorithm*is based on*an*approach due to Barvinok for*approximating*evaluations of a*polynomial*based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing ... We establish a deterministic*polynomial*-time*approximation*scheme for the partition function when the*interactions*and external fields are absolutely bounded close to zero. ... Now observe that*an*additive*approximation*of the logarithm of a*polynomial*corresponds to a multiplicative*approximation*of the*polynomial*. ...##
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Computational communicative algebra

2006
*
Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06
*

This is accomplished through

doi:10.1145/1145768.1145771
dblp:conf/issac/Poulisse06
fatcat:hbkgd5rpwnghzb6ejxnxkbi3aa
*an**Approximate*Border Basis*Algorithm*. ...*An*interpretation of the*Approximate*Vanishing Ideal is that it reveals*polynomial*identities that are almost satisfied over the set of points under consideration. ...##
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Fast Evaluation of Radial Basis Functions: Moment-Based Methods

1998
*
SIAM Journal on Scientific Computing
*

Adaptive

doi:10.1137/s1064827595293569
fatcat:5nz2h2cusvht3bwcns4sy3zv3m
*polynomial**approximation*. In this section we outline*an*adaptive method for constructing the*polynomial**approximations*to φ required at various stages in the*algorithm*. ... Calculate*an*error*polynomial**approximation*q 2 to φ on the interval [ 1 4 , 1]. Set = 2 and h 2 = degree(q 2 ). Step 2 If there are panels at level Create*interaction*and peer lists. ... Table 2 Degree of the economized*polynomial*sufficient to yield the specified absolute accuracy when*approximating*φ on the given interval. φ Interval Accuracy From equations (B.1), (B.2), and the uniqueness ...##
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Factoring games to isolate strategic interactions

2007
*
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07
*

We give

doi:10.1145/1329125.1329207
dblp:conf/atal/DavisBCS07
fatcat:net5zroknzg35h7iaglhrgstve
*an*expected*polynomial*time*algorithm*to divide a boundedpayout normal form game into factor games that isolate independent strategic*interactions*. ... We also show that the best*approximate*factoring can be found in*polynomial*time for a specific*interaction*that is not fully independent. ... We outlined a*polynomial*time*algorithm*for finding the minimal ǫ-factoring that isolates a specific*interaction*. ...##
###
Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

2019
*
Quantum
*

Our

doi:10.22331/q-2019-07-11-162
fatcat:po75rwjtkfcrzgr2iock3f3fwi
*algorithm*is based on*an*approach due to Barvinok for*approximating*evaluations of a*polynomial*based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing ... We establish a deterministic*polynomial*-time*approximation*scheme for the partition function when the*interactions*and external fields are absolutely bounded close to zero. ... Now observe that*an*additive*approximation*of the logarithm of a*polynomial*corresponds to a multiplicative*approximation*of the*polynomial*. ...##
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On the approximation of protein threading

1997
*
Proceedings of the first annual international conference on Computational molecular biology - RECOMB '97
*

Since this problem was already proved to be NP-hard, we study

doi:10.1145/267521.267523
dblp:conf/recomb/AkutsuM97
fatcat:6ivdlmrhffdopf5hgpoiwhn2dm
*polynomial*time*approximation**algorithms*. ... We also show*approximation**algorithms*for a special case and a general case, where a graph representing*interactions*between amino acid residues is restricted to be planar in a special case. ... Identifying B-strands is also*an*important problem in molecular biology. In this paper, we consider*polynomial*time*approximation**algorithms*. ...##
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On the approximation of protein threading

1999
*
Theoretical Computer Science
*

Since this problem was already proved to be NP-hard, we study

doi:10.1016/s0304-3975(98)00089-9
fatcat:pnalsqloonfddejq42mslhocqm
*polynomial*time*approximation**algorithms*. ... We also show*approximation**algorithms*for a special case and a general case, where a graph representing*interactions*between amino acid residues is restricted to be planar in a special case. ... Identifying B-strands is also*an*important problem in molecular biology. In this paper, we consider*polynomial*time*approximation**algorithms*. ...##
###
Generating function approximations at compile time

2006
*
2006 Fortieth Asilomar Conference on Signals, Systems and Computers
*

This may have some drawbacks: first in frequent cases, it is a compound function (e.g. log(1 + exp(−x))) that is needed, so that directly building a

doi:10.1109/acssc.2006.354761
fatcat:sbuqgbyxlzg3pbq7vo3rmaemh4
*polynomial*or rational*approximation*for that function ... We investigate the possibility of directly building accurate*approximations*at compile-time. ... ACKNOWLEDGEMENTS Nicolas Brisebarre, Sylvain Chevillard and Christoph Lauter provided some of the examples presented here, and did a great work on*polynomial**approximation*generation. ...##
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Computational complexity of loss networks

1994
*
Theoretical Computer Science
*

We also show that a general

doi:10.1016/0304-3975(94)90293-3
fatcat:44z3vrhzvjaebmp4jidukaq4lu
*algorithm*for*approximating*the blocking probabilities is also intractable unless RP=NP, which seems unlikely according to current common notions in complexity theory. ... In this paper we examine the theoretical limits on developing*algorithms*to find blocking probabilities in a general loss network. ... Suppose such*an**algorithm*existed. Then we use it to create*an*fpras for l/( 1 -L,) as follows. Given*an*E',*approximate*L, with the*algorithm*above using E = &l/2. ...##
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Approximability of the Ground State Problem for Certain Ising Spin Glasses

1997
*
Journal of Complexity
*

There is

doi:10.1006/jcom.1997.0449
fatcat:ghrd2c2ufzbufpkicsfwzaymle
*an**approximate**polynomial*time*algorithm*with absolute error less than n γ for all n; there exists a constant β > 0 such that every*approximate**polynomial*time*algorithm*has absolute error greater ... There is*an**approximate**polynomial*time*algorithm*with absolute error less than n/lg n; there exists a number k > 1 such that every*approximate**polynomial*time*algorithm*has absolute error greater than ... Given a*polynomial*-time*approximation**algorithm*A for GROUND STATE(γ), we construct*an**algorithm*A for GROUND STATE( 1 2 ) as follows.*ALGORITHM*A . ...##
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Sparse pseudorandom distributions

1992
*
Random structures & algorithms (Print)
*

*polynomial*-time

*algorithms*. ... Any

*polynomial*-time

*algorithm*trying to find a string in their support will succeed with negligible probability. ... We say that

*an*

*interactive*proof is zero-knowledge if for all probabilistic

*polynomial*-time machines V * , there exists a probabilistic

*polynomial*-time

*algorithm*Mr (called a sirnulafor) that on input ...

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Complexity of Discrete Energy Minimization Problems
[article]

2016
*
arXiv
*
pre-print

This paper can help vision researchers to select

arXiv:1607.08905v1
fatcat:k5xddu3xvndnziljktxo5p4mpe
*an*appropriate model for*an*application or guide them in designing new*algorithms*. ... This finding rules out the existence of any*approximation**algorithm*with a sub-exponential*approximation*ratio in the input size for these two problems, including constant factor*approximations*. ... Given*an*optimization problem P = (I, S, m, goal)*an**algorithm*A is*an**approximation**algorithm*for P if, for any given instance x ∈ I, it returns*an**approximate*solution, that is a feasible solution A( ...##
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Modeling opponent decision in repeated one-shot negotiations

2005
*
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems - AAMAS '05
*

In this paper, we present a learning mechanism using Chebychev's

doi:10.1145/1082473.1082534
dblp:conf/atal/SahaBS05
fatcat:x2e3gfb4bvcu3jwhp7mt3gxbua
*polynomials*by which*an*agent can*approximately*model the decision function used by the other agent based on the decision history of its ... Typically, these*interactions*take place under incomplete information, i.e.,*an*agent does not know exactly which offers may be acceptable to its opponent or what other outside options are available to ... Acknowledgements: This work has been supported in part by*an*NSF award IIS-0209208. ...
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