Interior-point methods for symmetric optimization based on a class of non-coercive kernel functions

In this paper, we generalize polynomial-time primal–dual interior-point methods for symmetric optimization based on a class of kernel functions, which is not coercive. The corresponding barrier functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like many usual barrier functions. Moreover, we analyse the accuracy of the algorithm for this class of functions and we obtain an upper bound for the accuracy which depends on a parameter of the class.