hey I'm trying to derive the dual of the following logarithmic barrier problem.
$min_{x∈R^n}$ $C^{T}x$ -$\sum_{i=0}^nlogx_i$
subject to $ a^{T}x$ = 0
I got the lagrange function L(x,λ,μ)=f(x)-$λ^{T}g(x)-μ^{T}h(x)$ and q(λ,μ)=inf$_{x∈R^n}$L(x,λ,μ).I replaced the constraint inequality for lambda ,but then I don't really know how to handle μ . I start by just cut it out form the lagrange function ( because of juste one constraint) but the I get stucked for the q function. It would be kind if someone could give me a hint .Thank you .