Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
CentER Working Paper Series No. 2011-060
25 Pages Posted: 2 Jun 2011
Date Written: May 26, 2011
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
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