A note on the continuity of solutions of parametric linear programs

A note on the continuity of solutions of parametric linear programs

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Article ID: iaor1991723
Country: Netherlands
Volume: 47
Issue: 1
Start Page Number: 143
End Page Number: 153
Publication Date: May 1990
Journal: Mathematical Programming (Series A)
Authors: ,
Abstract:

This note shows that, if a parametric linear program, min{cx:Ax=b1θ+b2,x≥0}, has optimal solutions in an interval [ℝ5θ,nθ] for θ, then, depending on degeneracy, the solutions s(θ) is a continuous vector function or a continuous point-to-set mapping. In the latter case an algorithm is introduced to solve the problem and generate a continuous vector solution in [ℝ5θ,nθ].

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