An entropy-like proximal algorithm and the exponential multiplier method for symmetric cone programming
نویسندگان
چکیده
We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to the symmetric cone constraint. The algorithm is based on a distance-like function that is an extension of the Kullback-Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithm for convex programming with nonnegative orthant cone constraint, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to enjoy properties similar to the exponential multiplier method in [29].
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