Checking solvability of systems of interval linear equations and inequalities via mixed integer programming

DOI10.1016/j.ejor.2008.11.008zbMath1176.90429OpenAlexW2040113346MaRDI QIDQ1042106

Oleg A. Prokopyev, Sergiy I. Butenko, Andrew C. Trapp

Publication date: 7 December 2009

Published in: European Journal of Operational Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejor.2008.11.008

zbMATH Keywords

solvabilitymixed integer programmingFarkas lemmainterval linear systems

Mathematics Subject Classification ID

Mixed integer programming (90C11)

Related Items (14)

Some results on the upper bound of optimal values in interval convex quadratic programming ⋮ Estimation of algebraic solution by limiting the solution set of an interval linear system ⋮ Farkas-type conditions of general interval linear systems for AE solvability ⋮ Some properties of the lower bound of optimal values in interval convex quadratic programming ⋮ On the algebraic solution of fuzzy linear systems based on interval theory ⋮ A new approach to obtain algebraic solution of interval linear systems ⋮ A note on absolute value equations ⋮ Checking weak optimality of the solution to linear programming with interval right-hand side ⋮ Solution types of two-sided interval linear system and their application on interval linear programming problems ⋮ A short note on solvability of systems of interval linear equations ⋮ Checking weak optimality of the solution to interval linear program in the general form ⋮ Solvability of Parametric Interval Linear Systems of Equations and Inequalities ⋮ EA solutions and EA solvability to general interval linear systems ⋮ The sparsest solution to the system of absolute value equations

Uses Software

• CPLEX

Cites Work

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• Strong solvability of interval linear programming problems
• Applications of interval computations. Proceedings of an international workshop, El Paso, TX, USA, February 23-25, 1995
• On the solution set of a linear equation with the right-hand side and operator given by intervals
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• On equivalent reformulations for absolute value equations
• Linear complementarity problems solvable by integer programming
• Zur lösung linearer ungleichungssysteme bei störimg der rechten seite und der koeffizientenmatrix
• Linear Programming with Inexact Data is NP‐Hard
• Solvability of Systems of Linear Interval Equations
• Linear Optimization Problems with Inexact Data

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