J. N. M. VAN LOON, Irreducibly inconsistent systems of linear inequalities, Eur. J. Oper. Res. 8 (1981), pp. 282--288. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On the Maximum Feasible Subsystem Problem, IISs and.. - Amaldi, Pfetsch.. (2002) (Correct)
....constraints as possible, which is the complementary version of MAX FS [19, 28, 39] In most situations this cannot be done by inspection and the need for effective algorithmic tools has become more acute with the considerable increase in model size. This type of questions was first addressed in [48]. The reader is referred to [27] for a survey on redundant and implied relations of inequality systems as well as on infeasibility issues. From the computational complexity point of view, MAX FS is NP hard [46] even when the matrix A is totally unimodular and b is integer; it can be approximated ....
J. N. M. VAN LOON, Irreducibly inconsistent systems of linear inequalities, Eur. J. Oper. Res. 8 (1981), pp. 282--288.
Infeasibility And Negative Curvature In Optimization - Boman (1999) (Correct)
....exists. The feasibility problem is as hard as NLP. Since SQP algorithms for nonlinear optimization linearize the nonlinear constraints, the linear case is most important to us. Some work has been done on identifying (irreducibly) inconsistent sets of constraints, mostly for linear inequalities [78, 8], but also for nonlinear programs [9] One motivation is 1.1. INFEASIBILITY ISSUES 5 Figure 1.1: An infeasible problem. that there may be errors in the formulation of a large optimization problem, and a tool that identi es a small set of inconsistent constraints can assist the user in detecting ....
J. van Loon. Irreducibly inconsistent systems of linear inequalities. European J. of Operations Research, 8:283-288, 1981.
About Infeasibility in the constraints of a Linear Model - Amaral (1999) (Correct)
....results regarding inequalities have been study by Carver, Motzkin and Fan. Two important results state that the number of relations (p) in an IIS cannot be greater then n 1, and the rank of the matrix of coecients must be p 1, where n is the dimension of the vector solution. A paper by Van Loon, [VLoo81] reviews some of the main results about IIS and presents the identi cation of IIS through a quasi simplex tableau. In the work of Hsiao Fan [HiFa92] the identi cation of rows in a quasi simplex tableau from which information about IIS could be obtained, was presented for a general problem with an ....
....chosen constraint should correspond to the one were the minimum of [A i ; b i ] v 0 is attained. The next example shows the implementation of this methodology, and in this particular case, the solution obtained is the optimal solution. Example 3. 2 Consider the following instance presented in [VLoo81]. 2 6 6 6 6 4 1 1 0 2 1 1 0 1 2 1 3 7 7 7 7 5 x 2 6 6 6 6 4 0 1 2 2 4 3 7 7 7 7 5 The SVD of the matrix C = A; b] is C = U V T where U = 2 6 6 6 6 4 0:0044 0:6108 0:3562 0:0790 0:7027 0:2777 0:6594 0:5728 0:2495 0:3127 0:4231 0:0008 0:2846 0:8274 ....
J. N. M. Van Loon, Irreducibly Inconsistent Systems of Linear Inequalities, EJOR, Vol. 8, pp. 282-288, 1981.
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