A sequential convex program method to DC program withjoint chance constraints
A sequential convex program method to DC program withjoint chance constraints
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DOI：
10.3934/jimo.2012.8.733
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发表时间：
2012-06
影响因子：
1.3
通讯作者：
X. Xiao;Jian Gu;Liwei Zhang;Shaowu Zhang
中科院分区：
文献类型：
--
作者：
X. Xiao;Jian Gu;Liwei Zhang;Shaowu Zhang
本文研究了一类具有联合机会约束的凸差分规划问题。我们提出了一个近似约束函数的DC函数和一个相应的DC程序（$\textrm{P}_{\varepsilon}$）来近似JCCDCP。在一些温和的假设下，我们证明了当$\varepsilon\向下0$时，问题（$\textrm{P}_{\varepsilon}$）的解收敛于JCCDCP的解。构造了一个顺序凸规划方法来解决问题（$\textrm{P}_{\varepsilon}$）。在每次迭代中，采用蒙特卡罗方法求解一个凸规划，并证明了生成的最优序列收敛于问题（$\textrm{P}_{\varepsilon}$）的平稳点。
In this paper, we consider a DC (difference of convex) programming problem with joint chance constraints (JCCDCP). We propose a DC function to approximate the constrained function and a corresponding DC program ($\textrm{P}_{\varepsilon}$) to approximate the JCCDCP. Under some mild assumptions, we show that the solution of Problem ($\textrm{P}_{\varepsilon}$) converges to the solution of JCCDCP when $\varepsilon\downarrow 0$. A sequential convex program method is constructed to solve the Problem ($\textrm{P}_{\varepsilon}$). At each iteration a convex program is solved based on the Monte Carlo method, and the generated optimal sequence is proved to converge to the stationary point of Problem ($\textrm{P}_{\varepsilon}$).