<p>This paper deals with the radius of robust feasibility for an adjustable robust linear inequality system with affine decision rules under general convex compact uncertain sets. The radius of robust feasibility is one notion of “size” that determines the largest size of the uncertain set such that the non-emptiness of the robust feasible set of this adjustable robust linear inequality system is guaranteed. We first present a linear inequality system reformulation for this adjustable robust linear inequality system with an affine decision rule. Then, we establish computable upper and lower bounds for the radius of robust feasibility for this adjustable robust linear inequality system with an affine decision rule. Moreover, as a special case, we also obtain an exact formula for calculating the radius of robust feasibility for a parametric linear homogeneous system with adjustable variables.</p>

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Radius of Robust Feasibility for Adjustable Robust Linear Inequality Systems with Affine Decision Rules

  • Xiangkai Sun,
  • Caiyun Xiao,
  • Xiaole Guo

摘要

This paper deals with the radius of robust feasibility for an adjustable robust linear inequality system with affine decision rules under general convex compact uncertain sets. The radius of robust feasibility is one notion of “size” that determines the largest size of the uncertain set such that the non-emptiness of the robust feasible set of this adjustable robust linear inequality system is guaranteed. We first present a linear inequality system reformulation for this adjustable robust linear inequality system with an affine decision rule. Then, we establish computable upper and lower bounds for the radius of robust feasibility for this adjustable robust linear inequality system with an affine decision rule. Moreover, as a special case, we also obtain an exact formula for calculating the radius of robust feasibility for a parametric linear homogeneous system with adjustable variables.