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On the Integrality Gap of Binary Integer Programs with Gaussian Data
[article]

2021
*
arXiv
*
pre-print

Building upon recent breakthrough work

arXiv:2012.08346v2
fatcat:clry6bhkofg7pbnx5q6jn6fp6u
*of*Dey, Dubey and Molinaro (SODA, 2021), we show that*the**integrality**gap*implies that branch-and-bound requires n^poly(m) time*on*random*Gaussian*IPs*with*good probability ... For a*binary**integer**program*(IP) max c^𝖳 x, Ax ≤ b, x ∈{0,1}^n, where A ∈ℝ^m × n and c ∈ℝ^n have independent*Gaussian*entries and*the*right-hand side b ∈ℝ^m satisfies that its negative coordinates have ...*On**the**Integrality**Gap**of**Binary**Integer**Programs**with**Gaussian**Data*37 We now sketch*the*high level ideas*of**the*proof*of*Lemma 16. ...##
###
MAP Clustering under the Gaussian Mixture Model via Mixed Integer Nonlinear Optimization
[article]

2020
*
arXiv
*
pre-print

An important benefit

arXiv:1911.04285v2
fatcat:svl7kad6qnc2xgch3i6aipbyjq
*of*our approach is*the*explicit quantification*of**the*degree*of*suboptimality, via*the*optimality*gap*, en route to finding*the*globally optimal MAP clustering. ... We approximate*the*MINLP through a mixed-*integer*quadratic*program*(MIQP) transformation that improves computational aspects while guaranteeing ϵ-global optimality. ... Maximum a posteriori clustering under*the**Gaussian*mixture model (1)*with*known covariance is a biconvex mixed-*integer*nonlinear*programming*optimization problem. Proof. ...##
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Support Vector Machines with the Ramp Loss and the Hard Margin Loss

2011
*
Operations Research
*

Based

doi:10.1287/opre.1100.0854
fatcat:hvderjcljbat7m6zvu7y7s767i
*on*results*on*simulated and real-world*data*, we conclude that SVM*with**the*ramp loss is preferred to SVM*with**the*hard margin loss. ... In*the*interest*of*deriving classifiers that are robust to outlier observations, we present*integer**programming*formulations*of*Vapnik's support vector machine (SVM)*with**the*ramp loss and hard margin ... ,*the**integrality**gap*is at least 94.1%. ...##
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Polynomial-time algorithms for the integer minimal principle for centrosymmetric structures

2005
*
Acta Crystallographica Section A Foundations of Crystallography
*

However,

doi:10.1107/s010876730501648x
pmid:15972998
fatcat:g5yfjhczlzdz7ldz3l5aw3rdda
*integer**programming*techniques may require an exponential number*of*iterations to exhaust*the*search space. ... Two specialized*Gaussian*elimination algorithms are then developed to solve this system*of*equations in polynomial time in*the*number*of*atoms. ... Yet computational experience*with**the**integer*minimal principle model indicates that*the**gap*between its optimal solution and its linear*programming*relaxation is zero. ...##
###
Second-Order Conic and Polyhedral Approximations of the Exponential Cone: Application to Mixed-Integer Exponential Conic Programs
[article]

2021
*
arXiv
*
pre-print

Since

arXiv:2106.09123v2
fatcat:gtxq3tru7jcfrebdgstg56c4x4
*the*exponential cone can be viewed as*the*epigraph*of*perspective*of**the*natural exponential function or*the*hypograph*of*perspective*of**the*natural logarithm function, many mixed-*integer*nonlinear ... To harvest*the*past efforts*on*MILPs and MISOCPs, this paper presents second-order conic (SOC) and poly-hedral approximation schemes for*the*exponential cone*with*application to MIECPs. ...*The**Gaussian*quadrature is quite accurate to approximate*one*-dimensional*integration*. In fact, according to Chapter 19 [24] ,*the*error*of**Gaussian*quadrature decays geometrically. ...##
###
Submodularization for Binary Pairwise Energies

2014
*
2014 IEEE Conference on Computer Vision and Pattern Recognition
*

Many computer vision problems require optimization

doi:10.1109/cvpr.2014.151
dblp:conf/cvpr/GorelickBVAD14
fatcat:4qjxhd3blvhitchofkco4dcafq
*of**binary*non-submodular energies. We propose a general optimization framework based*on*local submodular approximations (LSA). ... These methods obtain state-*of*-*the*-art results*on*a wide range*of*applications outperforming many standard techniques such as LBP, QPBO, and TRWS. ... Figures 3 (top-left) shows a*binary*image after convolution*with*a uniform 3 × 3 and adding*Gaussian*noise (σ = 0.05).*The*goal*of**binary*deconvolution is to recover Figure 5 . ...##
###
Cyclic coded integer-forcing equalization

2010
*
2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
*

Explicit bounds

doi:10.1109/allerton.2010.5706944
fatcat:inqiuwfstvde5kmp5tvbnexhrq
*on**the*performance*of**the*proposed scheme are derived. ... A discrete-time intersymbol interference (ISI) channel*with*additive*Gaussian*noise is considered, where only*the*receiver has knowledge*of**the*channel impulse response. ... ACKNOWLEDGMENT*The*authors wish to thank J. Zhan, B. Nazer, and M. Gastpar for discussions*on*IF equalization. They also thank Y. Kochman for helpful comments. ...##
###
Cyclic-Coded Integer-Forcing Equalization

2012
*
IEEE Transactions on Information Theory
*

Explicit bounds

doi:10.1109/tit.2012.2202633
fatcat:bxwo5xvukngrha2hsbppdodw7y
*on**the*performance*of**the*proposed scheme are derived. ... A discrete-time intersymbol interference (ISI) channel*with*additive*Gaussian*noise is considered, where only*the*receiver has knowledge*of**the*channel impulse response. ... ACKNOWLEDGMENT*The*authors wish to thank J. Zhan, B. Nazer, and M. Gastpar for discussions*on*IF equalization. They also thank Y. Kochman for helpful comments. ...##
###
Submodularization for Quadratic Pseudo-Boolean Optimization
[article]

2014
*
arXiv
*
pre-print

Many computer vision problems require optimization

arXiv:1311.1856v2
fatcat:xq5e5f7x6jgadp2zizpzh5uuai
*of**binary*non-submodular energies. We propose a general optimization framework based*on*local submodular approximations (LSA). ... These methods obtain state-*of*-*the*-art results*on*a wide range*of*applications outperforming many standard techniques such as LBP, QPBO, and TRWS. ... Overview*of*submodularization Linearization has been a popular approximation approach to*integer*quadratic problem (1)-(2), but it often requires relaxation leading to*the**integrality**gap*problem. ...##
###
Phase identification in smart grids

2011
*
2011 IEEE International Conference on Smart Grid Communications (SmartGridComm)
*

Furthermore, as

doi:10.1109/smartgridcomm.2011.6102329
dblp:conf/smartgridcomm/AryaSKDPHK11
fatcat:6yjitb4slvbfjieh447qubjhke
*the*number*of*measurements increase, continuous relaxations*of**integer**programs*may also be used to retrieve household phase efficiently. ... Our methods involve*the*use*of**integer**programming*and solutions can be retrieved using branch and bound search algorithms implemented by MIP solvers such as CPLEX. ... Then*one*could find all solutions X*with*a relative optimality*gap**of*α = {g(X)−g(X * )}/g(X). α can be set close to 0, for e.g 5%. ...##
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Integrated optimization of stope boundary selection and scheduling for sublevel stoping operations

2016
*
Journal of the Southern African Institute of Mining and Metallurgy
*

Randomly generated

doi:10.17159/2411-9717/2016/v116n12a7
fatcat:ijmzi2xspngfnjgkb7acscw6mq
*data*-sets for gold-copper mineralization are used to investigate*the*model performance, describing solution time as a function*of**data*complexity.*integer**programming*, operations research ...*the*typical processing power*of*onsite technical services systems,*on*standard size*data*-sets (Little, 2012). ... These problems are a subset*of*IP and are termed*binary**integer**programming*(BIP). ...##
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Polynomial algorithms for LP over a subring of the algebraic integers with applications to LP with circulant matrices

1992
*
Mathematical programming
*

We show that a modified variant

doi:10.1007/bf01581077
fatcat:5qj4mv6bdnguzaykwvnymw5oua
*of**the*interior point method can solve linear*programs*(LPs) whose coefficients are real numbers from a subring*of**the*algebraic*integers*. ... We then extend*the*Tardos scheme to our case, obtaining a running time which is independent*of**the*objective and right-hand side*data*. ... Acknowledgement This research was funded by*the*National Science Foundation DMS8810192. We greatly appreciate this financial support. under grant ...##
###
Near-optimal quantization and linear network coding for relay networks
[article]

2012
*
arXiv
*
pre-print

We prove that this digital interface is near-optimal for

arXiv:1203.2316v1
fatcat:t7nxrqxn7vdpbk7p4p2pxuulvy
*Gaussian*relay networks and*the*capacities*of**the**Gaussian*and*the*discrete networks are within a bounded*gap**of*O(M^2) bits, where M is*the*number ...*the*network within a bounded*gap**of**the*network's capacity. ... In this section, we start*the**program**of*approximating*Gaussian*networks*with**the*discrete model by proving that*the*cut-set bounds*of**the*two networks are within a bounded*gap*. ...##
###
TI-Stan: Model Comparison Using Thermodynamic Integration and HMC

2019
*
Entropy
*

Existing successful implementations use

doi:10.3390/e21121161
fatcat:blg5ypvhxbhl3d644w7vtvwofa
*binary*slice sampling*on**the*Hilbert curve to accomplish this task. ... MC-Stan uses automatic differentiation to compute*the*gradients*of**the*likelihood that HMC requires in about*the*same amount*of*time as it computes*the*likelihood function itself, easing*the**programming*... Within*the*TI-based methods proposed here, parameters are always represented as either*integer*values*on*[0, 2 B ] (for TI*with**Binary*Slice Sampling) or floating point values*on**the*interval [0, 1] (for ...##
###
An algorithm for generating stochastic cloud fields from radar profile statistics

2004
*
Atmospheric research
*

*The*stochastic cloud generation algorithm is tested

*with*3 months

*of*boundary layer cumulus cloud

*data*from an 8.6-mm wavelength radar

*on*

*the*island

*of*Nauru. ...

*The*major assumptions

*of*

*the*algorithm are that

*the*statistics

*of*

*the*fields are translationally invariant in

*the*horizontal and independent

*of*horizontal direction; however,

*the*statistics do depend

*on*...

*The*rest

*of*

*the*Nauru

*data*were obtained from

*the*Atmospheric Radiation Measurement (ARM)

*Program*sponsored by

*the*U.S. ...

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