# Complexity of necessary efficiency in interval linear programming and multiobjective linear programming

@article{Hladk2012ComplexityON,
title={Complexity of necessary efficiency in interval linear programming and multiobjective linear programming},
journal={Optimization Letters},
year={2012},
volume={6},
pages={893-899}
}
• Published 1 June 2012
• Mathematics
• Optimization Letters
We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x* is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the case of only one objective. Provided that x* is a non-degenerate basic solution, the problem is…
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## References

SHOWING 1-10 OF 30 REFERENCES

### On necessarily efficient solutions in interval multiobjective linear programming

We investigate multiobjective linear programming problems with objective coefficients varying inside given intervals. A feasible solution x ∗ is called necessarily efficient if it is efficient for

### Computing the tolerances in multiobjective linear programming

A procedure computing a tolerance for each objective function coefficient, such that all these coefficients may simultaneously and independently vary within their tolerances while preserving the efficiency of x*.

### Linear Multiple Objective Problems with Interval Coefficients

In this paper we consider linear multiple objective programs with coefficients of the criteria given by intervals. This class of problems is of practical interest since in many instances it is

### Strong Unboundedness of Interval Linear Programming Problems

• J. Koničková
• Mathematics
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)
• 2006
A linear programming problem whose coefficients are prescribed by intervals is called strongly unbounded if each linear programming problem obtained by fixing coefficients in these intervals is

### An interactive method of tackling uncertainty in interval multiple objective linear programming

• Computer Science
• 2009
The presented procedures provide a global view of the solutions in the best and worst case coefficient scenarios and allow performing the search for new solutions according to the achievement rates of the objective functions regarding both the upper and lower bounds.