Second-order cone programming: Difference between revisions

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==Example: Robust Linear Programming==

Consider a stochastic linear program in inequality form

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

: <math>P(a_i^T(x) \leq b_i) \leq \eta, \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>. We require that each constraint <math>a_i^T x \leq b_i </math> hold with a probability exceeding <math>\eta</math>, whereand <math>\eta\geq0.5</math>, i.e. <math>P(a_i^T x \leq b_i ) \geq \eta </math>. This problem can be expressed as the SOCP

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