随机规划问题的最优值和最优解集的稳定性

Stability of optimal values and optimal solution sets of stochastic programming

引进了局部化形式的概念,研究了随机规划问题的局部化最优解集和局部化最优值关于概率分布μ的定量稳定性,讨论了随机规划问题局部化最优值关于概率分布μ的连续性及局部化最dξ,优解集的Berge上半连续性.结果表明,当随机规划问题的局部化最优解惟一,且在ξnE‖ξn‖=E‖ξ‖的条件下,随机规划P(ξn)的局部化最优值收敛于P(ξ)的局部化最优limn→∞值,随机规划P(ξn)的局部化最优解集的任一选择收敛于随机规划问题的局部化惟一最优解.

By introducing the concept of localized version, the quantitative stability of localized optimal values and solution sets of stochastic programming with respect to the probability distribution μ is studied, and both the continuity of localized optimal values and the Berge upper-semicontinuous of localized optimal solution sets at μ of stochastic programming are discussed. Particularly, under the condition of ξ_ndξ,(lim)n→∞E‖ξ_n‖=E‖ξ‖, the localized optimal values of stochastic programming P(ξ_n) is converged in the localized optimal values of P(ξ), and all selections of localized optimal solution sets of P(ξ_n) are converged in the unique localized optimal solution of stochastic programming, provided that the localized optimal solution of stochastic programming is unique.