Abstract
Consider the general linear programming problem
, where \( {A_{ij}} = \left\{ {{{\left( {{a_{ij}}} \right)}_{rl}},r = \overline {1,{m_i}} ,l = \overline {1,{n_j}} } \right\} \), is a matrix of dimension \( _j,{c_j} = \left( {c_j^1,...,c_j^{{n_j}}} \right) \in {E^{{n_j}}},\;{b_i} = \left( {b_i^1,...,b_i^{mi}} \right) \in {E^{{m_i}}},\;i,j = 1,2,\;c = \left( {{c_1},{c_2}} \right),\;b = \left( {{b_1},{b_2}} \right) \). Let X ≠ ∅, f * = inf x ∈X f(x) > -∞. Then, according to Theorem 2.1.1, the set X * = {x ∈ X: f(x) = f *} is nonempty. Assume that instead of the exact initial data A ij , c j , b i we are only given their approximations \( {A_{ij}}(\delta ) = \left\{ {{{\left( {{a_{ij}}(\delta )} \right)}_{rl}},\;r = \overline {1,{m_i}} ,\;l = \overline {1{n_j}} } \right\},\;{c_j}(\delta ) = (c_j^1(\delta ),...,c_j^{{n_j}}),\;{b_i}(\delta ) = (b_i^1(\delta ),...,b_i^{{m_i}}(\delta )) \) such that
, where the quantity δ > 0 is an error in the assignment of the initial data.
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© 2001 Springer Science+Business Media Dordrecht
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Vasilyev, F.P., Ivanitskiy, A.Y. (2001). Criterion of Stability. In: In-Depth Analysis of Linear Programming. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9759-3_4
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DOI: https://doi.org/10.1007/978-94-015-9759-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5851-5
Online ISBN: 978-94-015-9759-3
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