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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.  ... 

A characterization of irreducible infeasible subsystems in flow networks

Imke Joormann, James B. Orlin, Marc E. Pfetsch
2016 Networks  
Written as a linear program, irreducible 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.  ... 
doi:10.1002/net.21686 fatcat:vgzhmsgvobdilhlrfucp5lebge

Some Structural and Algorithmic Properties of the Maximum Feasible Subsystem Problem [chapter]

Edoardo Amaldi, Marc E. Pfetsch, Leslie E. Trotter
1999 Lecture Notes in Computer Science  
vectors 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.  ... 
doi:10.1007/3-540-48777-8_4 fatcat:bvzynb4vxfhofgtjtjyxdcktlq

On the maximum feasible subsystem problem, IISs and IIS-hypergraphs

Edoardo Amaldi, Marc E. Pfetsch, Leslie E. Trotter, Jr.
2003 Mathematical programming  
We consider the MAX FS problem: For a given 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.  ... 
doi:10.1007/s10107-002-0363-5 fatcat:x3e5l7bzz5cu7orhq3zidvh36y

On Infeasibility of Systems of Convex Analytic Inequalities

Wiesława T. Obuchowska
1999 Journal of Mathematical Analysis and Applications  
In this paper we address the problem 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.  ... 
doi:10.1006/jmaa.1999.6357 fatcat:orimt7q3jvaqznsyjwepydd62m

Generating all vertices of a polyhedron is hard

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich
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 (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  ... 
doi:10.1145/1109557.1109640 fatcat:tbmwzijiq5codeswcznstn4acy

A Branch and Cut Algorithm for the Halfspace Depth Problem [article]

David Bremner, Dan Chen
2009 arXiv   pre-print
Irreducible 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.  ... 
arXiv:0910.1923v1 fatcat:q7tvc72gg5aurfw6c6bvgwgzam

Generating All Vertices of a Polyhedron Is Hard

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich
2007 Discrete & Computational Geometry  
As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an 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  ... 
doi:10.1007/s00454-006-1259-6 fatcat:4oausme7ejfolhbegnti222y74

Generating All Vertices of a Polyhedron Is Hard

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich
2008 Discrete & Computational Geometry  
As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an 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  ... 
doi:10.1007/s00454-008-9050-5 fatcat:s5been3h6bcnthbkmvkbhks3m4

Branch-and-Cut for the Maximum Feasible Subsystem Problem

Marc E. Pfetsch
2008 SIAM Journal on Optimization  
Key words and phrases. 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.  ... 
doi:10.1137/050645828 fatcat:w7syhnzs75fm7dgd2tpbn3pyae

A Greedy Approach to Identification of Piecewise Affine Models [chapter]

Alberto Bemporad, Andrea Garulli, Simone Paoletti, Antonio Vicino
2003 Lecture Notes in Computer Science  
The procedure that we propose for PWA identification exploits a greedy strategy for partitioning an 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  ... 
doi:10.1007/3-540-36580-x_10 fatcat:sjsvjznwqbfq3cc65v6ifu3trm

A bounded-error approach to piecewise affine system identification

A. Bempora, A. Garulli, S. Paoletti, A. Vicino
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).  ... 
doi:10.1109/tac.2005.856667 fatcat:oxqe4r23ordipptwdyl75a5pem

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

Okafor Ekene Gabriel, Sun Youchao, Uhuegho Osaretin Kole
2013 Research Journal of Applied Sciences Engineering and Technology  
A complex system comprising 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.  ... 
doi:10.19026/rjaset.6.3477 fatcat:6gd6da3cubhjnofuak4f2w53ra

Differential geometry tools for multidisciplinary design optimization, part II: application to QSD

Craig Bakker, Geoffrey T. Parks
2014 Structural And Multidisciplinary Optimization  
Now that convergence to feasibility has been established, the next step is to investigate the optimization performance 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).  ... 
doi:10.1007/s00158-014-1170-3 fatcat:mnmuwiyahjgc7lrhqulukdchbi

The MIN PFS problem and piecewise linear model estimation

Edoardo Amaldi, Marco Mattavelli
2002 Discrete Applied Mathematics  
We consider a new combinatorial optimization problem related to linear systems (MIN PFS) that consists, given an 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 .  ... 
doi:10.1016/s0166-218x(01)00260-8 fatcat:mbk3esqq55d4bnv7ox3frbcl4y
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