Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs

M. A. Goberna (), V. Jeyakumar () and G. Li ()
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M. A. Goberna: University of Alicante
V. Jeyakumar: University of New South Wales
G. Li: University of New South Wales

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 2, No 11, 597-622

Abstract: Abstract The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This determines when the robust feasible set is non-empty. Otherwise, the robust counterpart of an uncertain program is not well defined as a robust optimization problem. In this paper, we address a key fundamental question of robust optimization: How to compute the radius of robust feasibility of uncertain linear conic programs, including linear programs? We first provide computable lower and upper bounds for the radius of robust feasibility for general uncertain linear conic programs under the commonly used ball uncertainty set. We then provide important classes of linear conic programs where the bounds are calculated by finding the optimal values of related semi-definite linear programs, among them uncertain semi-definite programs, uncertain second-order cone programs and uncertain support vector machine problems. In the case of an uncertain linear program, the exact formula allows us to calculate the radius by finding the optimal value of an associated second-order cone program.

Keywords: Linear conic programs; Semi-definite programs; Parametric optimization; Robust feasibility (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01846-7

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