Sensitivity analysis in linear programming and semidefinite programming using interior-point methods | Zendy

E. Alper Yıldırım | Zendy; Michael D. Todd | Zendy

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Sensitivity analysis in linear programming and semidefinite programming using interior-point methods

Author(s) -

E. Alper Yıldırım,

Michael D. Todd

Publication year - 2001

Publication title -

mathematical programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.358

H-Index - 131

eISSN - 1436-4646

pISSN - 0025-5610

DOI - 10.1007/pl00011423

Subject(s) - interior point method , semidefinite programming , mathematics , linear programming , point (geometry) , mathematical optimization , sensitivity (control systems) , geometry , electronic engineering , engineering

. We analyze perturbations of the right-hand side and the cost parameters in linear programming (LP) and semidefinite programming (SDP). We obtain tight bounds on the perturbations that allow interior-point methods to recover feasible and near-optimal solutions in a single interior-point iteration. For the unique, nondegenerate solution case in LP, we show that the bounds obtained using interior-point methods compare nicely with the bounds arising from using the optimal basis. We also present explicit bounds for SDP using the Monteiro-Zhang family of search directions and specialize them to the AHO, H..K..M, and NT directions.

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