In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefinite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity analysis of the algorithms which use analogous strategy in [ 5 ]to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methods were obtained, namely, O( qn(p+q)/q(p+1)) log n/ε and O( q2√n) log n/ε, respectively.