概率约束优化问题的一个光滑D.C.近似

A smooth D.C.approximation of probabilistic constrained optimization problems

概率约束优化问题通常是非凸且非光滑的,因而在数值计算上存在困难.基于Pinar-Zenios光滑和函数,建立了概率约束优化问题的一个光滑D.C.近似问题,提出了求解光滑D.C.近似问题的序列凸近似(SCA)算法,分析了初始解的选取方法,并讨论了算法的收敛性,收敛定理表明可以由SCA算法可以得到光滑D.C.近似问题的KKT点,并且在迭代过程中,确保了由SCA算法生成的解序列的极限点是近似问题的KKT点.

Probabilistic constrained optimization problems are usually non\|convex and non\|smooth,so there are some difficulties in numerical calculation.A smooth D.C.approximation of probabilistic constrained optimization problems is established based on Pinar\|Zenios smooth plus function.Sequential convex approximation(SCA)algorithms for solving smooth D.C.approximation problems are proposed.The selection method of initial solutions is analyzed and the convergence of the algorithm is discussed.The convergence theorem shows that the KKT point of the smooth D.C.approximation problem can be obtained by sequential convex approximation(SCA)algorithm.It is ensured that the limit point of the solution sequence generated by the sequence convex approximation(SCA)algorithm is a KKT point of the approximate problem in the iterative process.