Robust sensitivity analysis for linear programming with ellipsoidal perturbation | Zendy

Ruotian Gao | Zendy; Wenxun Xing | Zendy

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Robust sensitivity analysis for linear programming with ellipsoidal perturbation

Author(s) -

Ruotian Gao,

Wenxun Xing

Publication year - 2019

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2019041

Subject(s) - ellipsoid , linear programming , perturbation (astronomy) , mathematical optimization , quadratic programming , sensitivity (control systems) , mathematics , convex optimization , regular polygon , linear matrix inequality , second order cone programming , feasible region , computer science , physics , geometry , quantum mechanics , astronomy , electronic engineering , engineering

Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our robust sensitivity analysis is to calculate the maximal radii of the perturbation sets to keep some properties of the robust feasible set. Mathematical models are formulated for the robust sensitivity analysis problems and all models are either reformulated into linear programs or convex quadratic programs except for the bi-convex programs where more than one row of the constraint matrix is perturbed. For the bi-convex programs, we develop a binary search algorithm.

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