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Small-dimensional linear programming and convex hulls made easy
1991
Discrete & Computational Geometry
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One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in Nd, d > 3, in expected time O(nln/2l). ...
In the linear programming algorithm the dependence of the time bound on d is of the form d!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses. ...
Convex Hulls This section concerns the construction of the convex hull of a set S of n points in Ne. ...
doi:10.1007/bf02574699
fatcat:r7enleuw3reohlgn7y3f5kvhza
A fast linear separability test by projection of positive points on subspaces
2007
Proceedings of the 24th international conference on Machine learning - ICML '07
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The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d < n 2 3 . ...
The worst case time complexity of the algorithm is O(nr 3 ) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. ...
Algorithms A general discussion of Linear Programming, Quadratic Programming, Convex Hull and the Perceptron Algorithms to solve the linear separability problem is included in this subsection. ...
doi:10.1145/1273496.1273586
dblp:conf/icml/YoganandaMG07
fatcat:y6rl3vw7wbgyfb47sbmvojel6m
Data-based polyhedron model for optimization of engineering structures involving uncertainties
2021
Data-Centric Engineering
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Then the vertex solution of convex polyhedron linear programming is presented and proven. ...
Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. ...
Similar to example 1, it is easy to prove that G is a convex polyhedron. Therefore (57) is a standard form of a convex polyhedron linear programming problem. ...
doi:10.1017/dce.2021.8
fatcat:t5ucgct6rrgetb6gaw6qrphx3q
Selecting texture discriminative descriptors of capsule endpscopy images
2009
2009 Proceedings of 6th International Symposium on Image and Signal Processing and Analysis
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In this paper we propose a new method for feature subset selection utilizing a convex hull (or convex polytope). ...
In supervised data classification one of the problems is to reduce dimensionality of feature vectors. ...
The next step is to find a centroid c of the convex hull. Then the convex hull is isotropically scaled up (cf. Fig. 1c) around the fixed centroid c of the convex hull. ...
doi:10.1109/ispa.2009.5297634
fatcat:ixcp7n47ujf7tavu2rv5mjnx3y
Learning to rank using 1-norm regularization and convex hull reduction
2010
Proceedings of the 48th Annual Southeast Regional Conference on - ACM SE '10
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However this approach increases the problem complexity from linear to quadratic in terms of sample size. We present in this paper a convex hull reduction method to reduce this impact. ...
We also propose a 1-norm regularization approach to simultaneously find a linear ranking function and to perform feature subset selection. The proposed method is formulated as a linear program. ...
Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation. ...
doi:10.1145/1900008.1900052
dblp:conf/ACMse/NanCDW10
fatcat:tzkeynse5jg2bkebyc7osgycdq
Human-machine interaction for real-time linear optimization
2012
2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
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Therefore, we propose a system providing the decision-makers with a convex hull of optimal solutions minimizing/maximizing the variables of interest. ...
These problems can be solved in less than an hour as they show a linear structure. ...
Its linear optimization problem is small and easy to solve -although it is of not as efficient as the heuristic methods. However, those three approaches meat our real-time expectations. ...
doi:10.1109/icsmc.2012.6377804
dblp:conf/smc/HamelGQBM12
fatcat:arzkzixr6zcpbf4cnkytgiluwi
A New Algorithm for 3D Reconstruction from Support Functions
2009
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In addition we offer a linear program version of the new algorithm that is much faster and better, or at least comparable, in performance at low levels of noise and reasonably small numbers of measurements ...
The algorithm, based on a least squares procedure, is very easy to program in standard software such as Matlab, and it works for both 2D and 3D reconstructions (in fact, in principle, in any dimension) ...
Then it is easy to check thatx 1 , . . . ,x k is also a solution of (8)- (9) , and the convex hull of {x 1 , . . . ,x k } is a possible output of the new support function algorithm. ...
doi:10.1109/tpami.2008.190
pmid:19147881
fatcat:6kj3suop6ng2rf4zm2qjbidcgq
Support vector machines
2000
SIGKDD Explorations
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The classification problem is used to investigate the basic concepts behind SVMs and to examine their strengths and weaknesses from a data mining perspective. ...
A B S T R A C T Support Vector Machines (SVMs) and related kernel methods have become increasingly popular tools for data mining tasks such as classification, regression, and novelty detection. ...
This work was performed with the support of the National Science Foundation under grants 970923 and IIS-9979860. ...
doi:10.1145/380995.380999
fatcat:mwuco6xjejhrjmcj7o4clqy6da
Computing convex hulls and counting integer points with polymake
2016
Mathematical Programming Computation
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The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. ...
Using the polymake system we explore various algorithms and implementations. Our experience in this area is summarized in ten "rules of thumb". ...
The comments by David Avis and Winfried Bruns were particularly detailed. ...
doi:10.1007/s12532-016-0104-z
fatcat:qk3iih53zfc3fdscu54lh6wwey
Geometric Reasoning with polymake
[article]
2005
arXiv
pre-print
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The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. ...
Later sections include a survey of research results obtained with the help of polymake so far and a short description of the technical background. ...
Linear programming. Polytopes most naturally appear as sets of feasible solutions of linear programs. Consider the following example.
Figure 2 . 2 Small linear program and a visualization. ...
arXiv:math/0507273v1
fatcat:tvougotxu5a73maybpwesr4p3q
Sequential convexification in reverse convex and disjunctive programming
1989
Mathematical programming
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each time the convex hull of the resulting set. ...
Here weextend the class of problems considered to disjunctive programs with infinitely many terms, also known as reverse convex programs, and give necessary and sufficient conditions for the ,-." solution ...
In a disjunctive 'K programming problem with finitely many terms in each disjunction, each g. is either linear or piecewise linear and convex. ...
doi:10.1007/bf01587096
fatcat:ezvkwghrt5dl7gmi4wzfpijeiu
Star splaying
2005
Proceedings of the twenty-first annual symposium on Computational geometry - SCG '05
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Star splaying is a general-dimensional algorithm that takes as input a triangulation or an approximation of a convex hull, and produces the Delaunay triangulation, weighted Delaunay triangulation, or convex ...
linear in the number of vertices. ...
Acknowledgments My thanks go to François Labelle for debunking a previous failed attempt at these results, and to Raimund Seidel for helpful discussions and for sharing his O( √ n) point location method ...
doi:10.1145/1064092.1064129
dblp:conf/compgeom/Shewchuk05
fatcat:yopblutnv5acjfgvun26cwvnq4
Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming
[article]
2022
arXiv
pre-print
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While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. ...
This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in d dimensions. ...
To reiterate, the convex hull of any set of d-dimensional points is the smallest convex set containing that set, and the convex hull is always closed in R d . ...
arXiv:2202.03572v1
fatcat:hjzvdg5icjdurf45piy76gitvq
On Functional Separately Convex Hulls
1998
Discrete & Computational Geometry
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Zhang on the existence of higher-dimensional nontrivial configurations of points and matrices). ...
We prove some results concerning the structure of functional D-convex hulls, e.g., a Krein-Milman-type theorem and a result on separation of connected components. ...
We also thank Pankaj Agarwal, Derick Wood, and Nati Linial for pointing out and/or providing relevant literature. ...
doi:10.1007/pl00009331
fatcat:gwcdua7ce5b5pdlqt6sx7fxoy4
Convex Hulls in a 3-Dimensional Space
[chapter]
2004
Lecture Notes in Computer Science
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This paper describes a new algorithm of computing the convex hull of a 3-dimensional object. ...
The convex hull generated by this algorithm is an abstract polyhedron being described by a new data structure, the cell list, suggested by one of the authors. ...
After sorting, the convex hull is computed by a recursive function consisting of two parts: generation of the convex hull of a small subset of points and merging two convex hulls. ...
doi:10.1007/978-3-540-30503-3_14
fatcat:22uhww5renh6tk3lnsx3ef2aaq
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