A full-step interior-point algorithm for second-order cone optimization based on a simple locally kernel function

In this paper, we investigate the properties of a simple locally kernel function. As an application, we present a full-step interior-point algorithm for second-order cone optimization (SOCO). The algorithm uses the simple locally kernel function to determine the search direction and define the neighbourhood of central path. The full step used in the algorithm has local quadratic convergence property according to the proximity function which is constructed by the simple locally kernel function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bound for SOCO.

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