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I'm studying the application of SOCP methods in Image restoration And I want to understand the difference between the two formulas of SOCP and how they are related. Standard form (1) :

min $f^{t}x $

subject to $\left \| A_{i}x + b_{i} \right \|_{{2}} \leq c^{{i}^{t}}x + d_{i}$

but also in some papers i found this standard form (2) :

min $c{_{1}}^{t}x_{1} + c{_{2}}^{t}x_{2} +. . . +c{_{r}}^{t}x_{r} $

$A_{1}x_{1}+ A_{2}x_{2} +...+A_{r}x_{r}=b$

  • What are the major differences between the two?

  • when and how should each one be applied?

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