We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. 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 algorithms for convex programming with nonnegative orthant cone constraints, 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 possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1–19, 1993) holds.
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机译：我们引入了一种类似熵的近端算法，以解决受对称锥约束的限制，使适当的凸函数最小化的问题。该算法基于类似距离的函数，该函数是Kullback-Leiber相对熵对对称圆锥体设置的扩展。类似于具有非负正圆锥约束的凸规划的近端算法，我们表明，在一些温和的假设下，该算法生成的序列是有界的，每个累加点都是所考虑问题的一个解决方案。此外，我们还将提出的算法双重应用到对称锥线性程序中，从而导致乘法器方法具有与指数乘法器方法相似的特性（Tseng和Bertsekas in Math。Program。60：1– （1993年第19卷）。
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