Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

A. Ben-Tal, D. den Hertog

Research output: Working paperDiscussion paperOther research output

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Volume2011-060
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-060

Fingerprint

Conic Optimization
Quadratic Optimization
Quadratic Constraint
Optimization Problem
Lemma
Convex Constraints
Linear Optimization
Robust Optimization
Uncertain Parameters
Quadratic Programming
Intersection
Uncertainty

Keywords

  • Conic Quadratic Program
  • hidden convexity
  • implementation error
  • robust optimization
  • simultaneous diagonalizability
  • S-lemma

Cite this

Ben-Tal, A., & den Hertog, D. (2011). Immunizing Conic Quadratic Optimization Problems Against Implementation Errors. (CentER Discussion Paper; Vol. 2011-060). Tilburg: Operations research.
Ben-Tal, A. ; den Hertog, D. / Immunizing Conic Quadratic Optimization Problems Against Implementation Errors. Tilburg : Operations research, 2011. (CentER Discussion Paper).
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Ben-Tal, A & den Hertog, D 2011 'Immunizing Conic Quadratic Optimization Problems Against Implementation Errors' CentER Discussion Paper, vol. 2011-060, Operations research, Tilburg.

Immunizing Conic Quadratic Optimization Problems Against Implementation Errors. / Ben-Tal, A.; den Hertog, D.

Tilburg : Operations research, 2011. (CentER Discussion Paper; Vol. 2011-060).

Research output: Working paperDiscussion paperOther research output

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AB - 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.

KW - Conic Quadratic Program

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KW - implementation error

KW - robust optimization

KW - simultaneous diagonalizability

KW - S-lemma

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Ben-Tal A, den Hertog D. Immunizing Conic Quadratic Optimization Problems Against Implementation Errors. Tilburg: Operations research. 2011. (CentER Discussion Paper).