I want to know the dual of this problem: \begin{equation} \begin{aligned} &\min_{x,t}f^Tx\\ s.t.&\|A_ix+b_i\|\le c_i^Tx+d_i\quad i=1,\dots,n\\ &\begin{bmatrix} C_0+\sum_{i=1}^nx_iC_i&Dx\\ x^TD&t \end{bmatrix}\succeq 0, \end{aligned} \end{equation} In fact, I know the first constraint is the second-order cone, but don't know how to solve the second constraint.
2026-03-30 05:28:56.1774848536
what's dual of this cone optimization problem, Is it a linear problem?
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