# individual vs joint constraints in stochastic programming

 0 In stochastic programming (SP), a common constraint is of the form $$\mathbb{P}(f(x,\xi) \leq 0) \geq \alpha.$$ If $$f$$ is affine in $$x$$ and $$\xi$$, then we have the chance constraint of the form $$\mathbb{P}(A(\xi)x + b(\xi)+ c \leq 0) \geq \alpha$$ for $$A\in \mathbb{R}^{m \times n}$$. In this case, we can represent the joint constraint with $$m$$ individual constraints of the form $$\mathbb{P}(a_i^T(\xi)x + b_i(\xi) + c \leq 0) \geq \alpha.$$ To confirm, we can do this because each dimension is independent? How can I better see this? Also, if $$f$$ were not linear in $$x$$ and $$\xi$$, then we are unable to separate the joint constraint into constraint components, right? A simple, introductory reference on this idea would be much appreciated! asked 19 Dec '17, 15:51 jjjjjj 31●4 accept rate: 0%
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