In this paper, we study a new parametric robust linear problem (PRLP) whose data are allowed to be perturbed not only on the objective and constraint functions but also on the size of the uncertainty sets. Using a dua...
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In this paper, we study a new parametric robust linear problem (PRLP) whose data are allowed to be perturbed not only on the objective and constraint functions but also on the size of the uncertainty sets. Using a dual approach, we examine the stability and sensitivity properties of PRLP by looking at how the behaviors of its optimal value function and solution map change according to the change of the parameters. More precisely, we examine the closedness and lower and upper semicontinuity of the solution map and the lower and upper semicontinuity as well as Lipschitz property of the optimal value function of PRLP varying around a reference parameter. In this way, we obtain the nonemptiness and boundedness of the solution sets and a characterization for the Lipschitz continuity of the optimal value function for semi-infinite linearprograms when fixing the corresponding index sets.
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 $$\left[ {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\theta } ,\bar \theta } \r...
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This note shows that, if a parametric linear program, min{cx: Ax = b 1 θ+b 2,x≥0}, has optimal solutions in an interval $$\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]$$ .
We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
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