Abstract
In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO problem. We then develop a primal–dual interior point algorithm for solving a type-2 second order conic optimization problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive a new iteration bound for our framework.
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