A note on the continuity of solutions of parametric linear programs

Abstract

This note shows that, if a parametric linear program, min{cx: Ax = b ₁ θ+b ₂,x≥0}, has optimal solutions in an interval$\left[ {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\theta } ,\bar \theta } \right]$ forθ, then, depending on degeneracy, the solutions(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$\left[ {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\theta } ,\bar \theta } \right]$.