Extending the scope of robust quadratic optimization

A. Marandi, A. Ben-Tal, D. den Hertog, B. Melenberg

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademic

Uittreksel

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in general, intractable. Hence, we derive tractable inner and outer approximations of the robust counterparts of such constraints. The approximations are made by replacing the quadratic terms in the uncertain parameters with suitable linear upper and lower bounds. Furthermore, when the uncertain parameters consist of a mean vector and covariance matrix, we construct a natural uncertainty set using an asymptotic confidence level and show that its support function is semi-definite representable. Finally, we apply our results to a portfolio choice, a norm approximation, and a regression line problem.
TaalEngels
Artikelnummer6017
TijdschriftOptimization Online
StatusGepubliceerd - 2017

Vingerafdruk

Covariance matrix
Uncertainty

Citeer dit

Marandi, A., Ben-Tal, A., den Hertog, D., & Melenberg, B. (2017). Extending the scope of robust quadratic optimization. Optimization Online, [6017].
Marandi, A. ; Ben-Tal, A. ; den Hertog, D. ; Melenberg, B./ Extending the scope of robust quadratic optimization. In: Optimization Online. 2017
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Extending the scope of robust quadratic optimization. / Marandi, A.; Ben-Tal, A.; den Hertog, D.; Melenberg, B.

In: Optimization Online, 2017.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademic

TY - JOUR

T1 - Extending the scope of robust quadratic optimization

AU - Marandi,A.

AU - Ben-Tal,A.

AU - den Hertog,D.

AU - Melenberg,B.

PY - 2017

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N2 - In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in general, intractable. Hence, we derive tractable inner and outer approximations of the robust counterparts of such constraints. The approximations are made by replacing the quadratic terms in the uncertain parameters with suitable linear upper and lower bounds. Furthermore, when the uncertain parameters consist of a mean vector and covariance matrix, we construct a natural uncertainty set using an asymptotic confidence level and show that its support function is semi-definite representable. Finally, we apply our results to a portfolio choice, a norm approximation, and a regression line problem.

AB - In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in general, intractable. Hence, we derive tractable inner and outer approximations of the robust counterparts of such constraints. The approximations are made by replacing the quadratic terms in the uncertain parameters with suitable linear upper and lower bounds. Furthermore, when the uncertain parameters consist of a mean vector and covariance matrix, we construct a natural uncertainty set using an asymptotic confidence level and show that its support function is semi-definite representable. Finally, we apply our results to a portfolio choice, a norm approximation, and a regression line problem.

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JO - Optimization Online

T2 - Optimization Online

JF - Optimization Online

M1 - 6017

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Marandi A, Ben-Tal A, den Hertog D, Melenberg B. Extending the scope of robust quadratic optimization. Optimization Online. 2017. 6017.