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Characterization of perturbed mathematical programs and interval analysis. (English) Zbl 0811.90102

Interval arithmetic was developed by R. E. Moore [‘Interval analysis’ (1966; Zbl 0176.133)] as a method to yield more precise numerical computations. Several authors have used interval arithmetic to deal with parametric or sensitivity analysis in mathematical programming problems.
In this paper, the authors present a characterization of perturbed convex programs and the resulting solution interval. Several examples of a non- intuitive behavior of perturbed convex problems are presented and it is illustrated how interval arithmetic deals with such situations.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
65G30 Interval and finite arithmetic

Citations:

Zbl 0176.133
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References:

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[9] R.E. Moore,Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1966). · Zbl 0176.13301
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