Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

CentER Working Paper Series No. 2011-060

25 Pages Posted: 2 Jun 2011  

Aharon Ben-Tal

Technion-Israel Institute of Technology

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: May 26, 2011

Abstract

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.

Keywords: conic quadratic program, hidden convexity, implementation error, robust optimization, simultaneous diagonalizability, S-lemma

JEL Classification: C61

Suggested Citation

Ben-Tal, Aharon and den Hertog, Dick, Immunizing Conic Quadratic Optimization Problems Against Implementation Errors (May 26, 2011). CentER Working Paper Series No. 2011-060. Available at SSRN: https://ssrn.com/abstract=1853320 or http://dx.doi.org/10.2139/ssrn.1853320

Aharon Ben-Tal

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000
Israel

Dick Den Hertog (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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