 (12)
 (13)
where  is a safety factor determined by  in our implementation. Note that  and  are the actual step sizes for dual and primal variables, respectively. In conventional algorithms,  is always set to 1. In this paper, it is determined by a backtracking filter line-search procedure which will be discussed later on.
Instead of changing barrier parameter at each iterate, the value of μ is kept intact until an approximate solution to the μ-barrier problem is obtained. The optimality error of a μ-barrier problem is defined as
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