On Unbounded Tolerable Solution Sets
نویسنده
چکیده
We prove that the nonempty tolerable solution set of the interval linear system Ax = b is unbounded if and only if the interval matrix of the system has linearly dependent degenerate columns. Also, we prove that the tolerable solution set may be represented as a sum of the linear subspace {c R | Ac = 0} and a bounded convex polyhedron and propose a way for suitable estimation of unbounded tolerable solution sets.
منابع مشابه
Numerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملOuter enclosures to the parametric AE solution set
We consider systems of linear equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters. We study parametric AE solution sets, which are defined by universally and existentially quantified parameters, and the former precede the latter. Based on a recently obtained explicit description of such solution sets, we present three approac...
متن کاملOn Unboundedness of Generalized Solution Sets for Interval Linear Systems
The work presents a necessary and sufficient condition for the generalized AE-solution sets to interval linear systems of equations to be unbounded. The criterion requires solvability of one of the totality of 2 linear inequalities constructed from the initial interval system. It is shown that the problem of recognizing the boundedness of AE-solution sets is NP-complete in general.
متن کاملUNBOUNDEDNESS IN MOILP AND ITS EFFICIENT SOLUTIONS
In this paper we investigate Multi-Objective Integer Linear Programming (MOILP) problems with unbounded feasible region and introduce recession direction for MOILP problems. Then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. Finally we present some examples with unbounded feasible region and fi...
متن کاملExplicit Description of AE Solution Sets for Parametric Linear Systems
Consider linear systems whose input data are linear functions of uncertain parameters varying within given intervals. We are interested in an explicit description of the so-called AE parametric solution sets (where all universally quantified parameters precede all existentially quantified ones) by a set of inequalities not involving the parameters. This work presents how to obtain explicit desc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Reliable Computing
دوره 11 شماره
صفحات -
تاریخ انتشار 2005