Second-order cone programming: Difference between revisions

Revision as of 17:09, 5 December 2007

Revision as of 17:10, 5 December 2007

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:minimize <math>\ c^T x \ </math> subject to

: <math>P(a_i^T(x) \leq b_i) \leqgeq \etap, \quad i = 1,\dots,m </math>

where the parameters <math>a_i \ </math> are independent Gaussian random vectors with mean <math>\bar{a}_i</math> and covariance <math>\Sigma_i \ </math> and <math>\etap\geq0.5</math>. This problem can be expressed as the SOCP

:minimize <math>\ c^T x \ </math> subject to

: <math>\bar{a}_i^T (x) + \Phi^{-1}(\eta1-p) \lVert \Sigma_i^{1/2} x \rVert_2 \leq b_i , \quad i = 1,\dots,m </math>

where <math>\Phi^{-1} \ </math> is the inverse [[error function]].