An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs

T. D. Chuong () and V. Jeyakumar ()
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T. D. Chuong: University of New South Wales
V. Jeyakumar: University of New South Wales

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 1, No 10, 203-226

Abstract: Abstract We present an exact formula for the radius of robust feasibility of uncertain linear programs with a compact and convex uncertainty set. The radius of robust feasibility provides a value for the maximal ‘size’ of an uncertainty set under which robust feasibility of the uncertain linear program can be guaranteed. By considering spectrahedral uncertainty sets, we obtain numerically tractable radius formulas for commonly used uncertainty sets of robust optimization, such as ellipsoids, balls, polytopes and boxes. In these cases, we show that the radius of robust feasibility can be found by solving a linearly constrained convex quadratic program or a minimax linear program. The results are illustrated by calculating the radius of robust feasibility of uncertain linear programs for several different uncertainty sets.

Keywords: Uncertain linear program; Robust linear optimization; Spectrahedron; Robust solution; Linear matrix inequality; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-017-1067-6

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