In this research, stochastic geometric programming with joint chance constraints is investigated with elliptically distributed random parameters. The constraint’s random coefficient vectors are considered dependent, and the dependence of the random vectors is handled through copulas. Moreover, Archimedean copulas are used to derive the random rows distribution. A convex approximation optimization problem is proposed for this class of stochastic geometric programming problems using a standard variable transformation. Furthermore, a piecewise tangent approximation and sequential convex approximation are employed to obtain the lower and upper bounds for the convex optimization model, respectively. Finally, an illustrative optimization example on randomly generated data is presented to demonstrate the efficiency of the methods and algorithms.

在这项研究中，使用椭圆分布的随机参数研究了具有联合机会约束的随机几何规划。约束的随机系数向量被认为是依赖的，随机向量的依赖是通过 copulas 处理的。此外，阿基米德联结用于推导随机行分布。针对这类使用标准变量变换的随机几何规划问题，提出了凸逼近优化问题。此外，采用分段切线近似和顺序凸近似来分别获得凸优化模型的下限和上限。最后，给出了随机生成数据的说明性优化示例，以证明方法和算法的效率。