This paper discusses joint rectangular chance or probabilistic constrained geometric programs. We present a new reformulation of the joint rectangular chance constrained geometric programs where the random parameters are elliptically distributed and pairwise independent. As this reformulation is not convex, we propose new convex approximations based on the variable transformation together with piecewise linear approximation methods. For the latter, we provide a theoretical bound for the number of segments in the worst case. Our numerical results show that our approximations are asymptotically tight.

中文翻译：

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矩形机会约束几何优化

本文讨论联合矩形机会或概率约束几何程序。我们提出了新的联合矩形机会约束几何程序的新公式，其中随机参数呈椭圆分布且成对独立。由于这种重构不是凸的，因此我们基于变量变换和分段线性逼近方法提出了新的凸逼近。对于后者，我们为最坏情况下的段数提供了理论上的界限。数值结果表明，我们的逼近是渐近严格的。