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Page 72 of The Journal of the Operational Research Society Vol. 47, Issue 1
[page]

1996
*
The Journal of the Operational Research Society
*

Ryan (1990)

*Identifying**minimally**infeasible**subsystems**of*equations. ORSA J. Computing 2, 61-63. . J. Ryan (1991) Transversals*of*I[S-hypergraphs. Congressus Numerantium 81, 17-22. . M. ... Ryan (1994) Finding the Maximum Weight Feasible*Subsystem**of*an*Infeasible*System*of*Linear*Inequalities*. Working paper, Mathematics Department, University*of*Colorado at Denver. . E. ALmacpi and V. ...##
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A characterization of irreducible infeasible subsystems in flow networks

2016
*
Networks
*

Written as a linear program, irreducible

doi:10.1002/net.21686
fatcat:vgzhmsgvobdilhlrfucp5lebge
*infeasible**subsystems*(IISs) provide a dierent means*of**infeasibility*characterization. ...*Infeasible*network ow problems with supplies and demands can be characterized via violated cut-*inequalities**of*the classical Gale-Homan theorem. ... Acknowledgement We thank the anonymous referees for their suggestions and the editor for his postitive handling*of*this paper. ...##
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Some Structural and Algorithmic Properties of the Maximum Feasible Subsystem Problem
[chapter]

1999
*
Lecture Notes in Computer Science
*

vectors

doi:10.1007/3-540-48777-8_4
fatcat:bvzynb4vxfhofgtjtjyxdcktlq
*of*feasible*subsystems**of*a given*infeasible*system. ... In this paper we examine structural and algorithmic properties*of*Max FS and*of*irreducible*infeasible**subsystems*(IISs), which are intrinsically related, since one must delete at least one constraint ... Ziegler for helpful discussions regarding the material*of*Section 3. ...##
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On the maximum feasible subsystem problem, IISs and IIS-hypergraphs

2003
*
Mathematical programming
*

We consider the MAX FS problem: For a given

doi:10.1007/s10107-002-0363-5
fatcat:x3e5l7bzz5cu7orhq3zidvh36y
*infeasible*linear system Ax ≤ b, determine a feasible*subsystem*containing as many*inequalities*as possible. ... Finally we investigate rank facets*of*the Feasible*Subsystem*polytope whose vertices are incidence vectors*of*feasible*subsystems**of*a given*infeasible*system. ... An*infeasible**subsystem*Σ*of*Σ is an Irreducible*Infeasible**Subsystem*(IIS) if every proper*subsystem**of*Σ is feasible. ...##
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On Infeasibility of Systems of Convex Analytic Inequalities

1999
*
Journal of Mathematical Analysis and Applications
*

In this paper we address the problem

doi:10.1006/jmaa.1999.6357
fatcat:orimt7q3jvaqznsyjwepydd62m
*of*the*infeasibility**of*systems defined by convex analytic*inequality*constraints. ... We analyze properties*of*the irreducible sets, as well as*infeasibility*sets in connection with the set K , showing in particular that every*infeasible*system contains an inconsistent*subsystem**of*cardinality ... status neither*of*the system (1.1) nor*of*its proper*subsystem*, so ( I \ K ) n U, Now we will consider a problem*of*the upper bound for the*minimal*cardinality*of*the irreducible*infeasible*sets. ...##
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Generating all vertices of a polyhedron is hard

2006
*
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
*

As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an (

doi:10.1145/1109557.1109640
fatcat:tbmwzijiq5codeswcznstn4acy
*infeasible*) system*of*linear*inequalities*, generating all*minimal**infeasible**subsystems*... Yet, for generating maximal feasible*subsystems*the complexity remains open. (ii) Given a (feasible) system*of*linear*inequalities*, generating all vertices*of*the corresponding polyhedron is hard. ... The problems*of*finding*minimal**infeasible**subsystems**of*a system*of*linear*inequalities*, sometimes called IIS (Irreducible Inconsistent*Subsystems*) or Helly systems, and its natural dual*of*finding maximal ...##
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A Branch and Cut Algorithm for the Halfspace Depth Problem
[article]

2009
*
arXiv
*
pre-print

Irreducible

arXiv:0910.1923v1
fatcat:q7tvc72gg5aurfw6c6bvgwgzam
*Infeasible**Subsystem*(IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more numerically stable. ... Computing halfspace depth is NP-hard, and it is equivalent to the Maximum Feasible*Subsystem*problem. ... Basic*infeasible**subsystem*cuts The paper [5] describes how to generate a basic*infeasible**subsystem*(BIS)*of*an*infeasible*system. ...##
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Generating All Vertices of a Polyhedron Is Hard

2007
*
Discrete & Computational Geometry
*

As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an

doi:10.1007/s00454-006-1259-6
fatcat:4oausme7ejfolhbegnti222y74
*infeasible*system*of*linear*inequalities*, generating all*minimal**infeasible**subsystems*... Yet, for generating maximal feasible*subsystems*the complexity remains open. (ii) Given a feasible system*of*linear*inequalities*, generating all vertices*of*the corresponding polyhedron is hard. ... The problems*of*finding*minimal**infeasible**subsystems**of*a system*of*linear*inequalities*, sometimes called IIS (Irreducible Inconsistent*Subsystems*) or Helly systems, and its natural dual*of*finding maximal ...##
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Generating All Vertices of a Polyhedron Is Hard

2008
*
Discrete & Computational Geometry
*

As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an

doi:10.1007/s00454-008-9050-5
fatcat:s5been3h6bcnthbkmvkbhks3m4
*infeasible*system*of*linear*inequalities*, generating all*minimal**infeasible**subsystems*... Yet, for generating maximal feasible*subsystems*the complexity remains open. (ii) Given a feasible system*of*linear*inequalities*, generating all vertices*of*the corresponding polyhedron is hard. ... The problems*of*finding*minimal**infeasible**subsystems**of*a system*of*linear*inequalities*, sometimes called IIS (Irreducible Inconsistent*Subsystems*) or Helly systems, and its natural dual*of*finding maximal ...##
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Branch-and-Cut for the Maximum Feasible Subsystem Problem

2008
*
SIAM Journal on Optimization
*

Key words and phrases.

doi:10.1137/050645828
fatcat:w7syhnzs75fm7dgd2tpbn3pyae
*infeasible*linear*inequality*system, irreducible*infeasible**subsystem*(IIS), maximum feasible*subsystem*problem, minimum IIS-cover, branch-and-cut. ... This paper presents a branch-and-cut algorithm for the NPhard maximum feasible*subsystem*problem: For a given*infeasible*linear*inequality*system, determine a feasible*subsystem*containing as many*inequalities*... Furthermore, he thanks Edoardo Amaldi and Pietro Belotti for providing the DVB instances*of*Section 4.3, and Gianni Codato and Matteo Fischetti for the data used in Section 4.4. ...##
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A Greedy Approach to Identification of Piecewise Affine Models
[chapter]

2003
*
Lecture Notes in Computer Science
*

The procedure that we propose for PWA identification exploits a greedy strategy for partitioning an

doi:10.1007/3-540-36580-x_10
fatcat:sjsvjznwqbfq3cc65v6ifu3trm
*infeasible*system*of*linear*inequalities*into a minimum number*of*feasible*subsystems*: this provides ... This problem involves the estimation from data*of*both the parameters*of*the affine submodels and the partition*of*the PWA map. ... In particular, the greedy strategy proposed in [8] for partitioning an*infeasible*system*of*linear*inequalities*into a minimum number*of*feasible*subsystems*, is exploited in order to provide an initial ...##
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A bounded-error approach to piecewise affine system identification

2005
*
IEEE Transactions on Automatic Control
*

*Subsystems*) for a suitable set

*of*linear complementary

*inequalities*derived from data. ... The first stage simultaneously classifies the data points and estimates the number

*of*submodels and the corresponding parameters by solving the MIN PFS problem (Partition into a MINimum Number

*of*Feasible ... Data are by courtesy

*of*Assembleon, Eindhoven (www.assembleon.com). ...

##
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Multi-Objective Optimization of a Complex System using GPSIA+DS

2013
*
Research Journal of Applied Sciences Engineering and Technology
*

A complex system comprising

doi:10.19026/rjaset.6.3477
fatcat:6gd6da3cubhjnofuak4f2w53ra
*of*mixed configuration, k-out-*of*-n and redundant*subsystem*was used to validate GPSIA+DS in comparison with Genetic Pareto Set Identification Algorithm (GPSIA) and Fast Non-Dominated ...*Infeasible*solutions could facilitate faster convergence to the true Pareto front. ... all b*inequality*and q equality constraints. ...##
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Differential geometry tools for multidisciplinary design optimization, part II: application to QSD

2014
*
Structural And Multidisciplinary Optimization
*

Now that convergence to feasibility has been established, the next step is to investigate the optimization performance

doi:10.1007/s00158-014-1170-3
fatcat:mnmuwiyahjgc7lrhqulukdchbi
*of*various QSD modifications. ... Our predictions regarding feasibility prove to be accurate: QSD does not return any feasible points, whereas all*of*the final design points from IDF and the modified QSD are feasible. ... Acknowledgments This research is supported by the Natural Sciences and Engineering Research Council*of*Canada (NSERC) and the Cambridge Commonwealth Trust and Cambridge Overseas Trust (CCT/COT). ...##
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The MIN PFS problem and piecewise linear model estimation

2002
*
Discrete Applied Mathematics
*

We consider a new combinatorial optimization problem related to linear systems (MIN PFS) that consists, given an

doi:10.1016/s0166-218x(01)00260-8
fatcat:mbk3esqq55d4bnv7ox3frbcl4y
*infeasible*system, in ÿnding a partition into a minimum number*of*feasible*subsystems*. ... the classical Agmon-Motzkin-Schoenberg relaxation method for solving systems*of*linear*inequalities*. ... Updating T 0 at the beginning*of*each random cycle corresponds to rescaling T with respect to the current |v| without a ecting the decrease*of*T given by . ...
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