辽宁师范大学学报（自然科学版）
遼寧師範大學學報（自然科學版）
료녕사범대학학보（자연과학판）
JOURNAL OF LIAONING NORMAL UNIVERSITY(NATURAL SCIENCE)
2013年
1期
7-10
,共4页
联合概率约束%Sigmoid函数%光滑近似%收敛性分析
聯閤概率約束%Sigmoid函數%光滑近似%收斂性分析
연합개솔약속%Sigmoid함수%광활근사%수렴성분석
joint chance constraints%Sigmoid function%smoothing approximation%convergence analysis
许多有重要价值的实际问题均属于概率约束问题,该类问题通常是非凸的且非光滑的,有效的求解方法多集中于凸近似方法.基于Sigmoid函数,将概率约束函数光滑化并建立相应的光滑近似问题,通过收敛性分析,证明了在适当的条件下,当参数充分大时,光滑近似问题与原问题等价,且光滑近似问题的最优值和最优解集分别收敛到原问题的最优值和最优解集.
許多有重要價值的實際問題均屬于概率約束問題,該類問題通常是非凸的且非光滑的,有效的求解方法多集中于凸近似方法.基于Sigmoid函數,將概率約束函數光滑化併建立相應的光滑近似問題,通過收斂性分析,證明瞭在適噹的條件下,噹參數充分大時,光滑近似問題與原問題等價,且光滑近似問題的最優值和最優解集分彆收斂到原問題的最優值和最優解集.
허다유중요개치적실제문제균속우개솔약속문제,해류문제통상시비철적차비광활적,유효적구해방법다집중우철근사방법.기우Sigmoid함수,장개솔약속함수광활화병건립상응적광활근사문제,통과수렴성분석,증명료재괄당적조건하,당삼수충분대시,광활근사문제여원문제등개,차광활근사문제적최우치화최우해집분별수렴도원문제적최우치화최우해집.
Many important practical problems can be formulated as chance constrained programs , which are usually non‐convex and non‐smooth .Effective methods for chance constrained programs mostly focus on convex approximation techniques .Based on Sigmoid function ,this paper proposes a smoothing function to approximate the chance constraints and builds the associated smoothed approx‐imation problem .The convergence analysis shows that the approximation problem is equivalent to the primal problem when parameter is large enough .In addition ,optimal value and the set of optimal so‐lutions of the smoothed approximation problem converge to optimal value and the set of optimal solu‐tions of chance constrained program under appropriate conditions ,respectively .
