摘要
半正定单调变分不等式CPC算法只需要计算迭代点的函数值,可以解决一类没有显式表达式的半正定单调变分不等式问题.最近A.Nemirovski(SIAM J Optimiz,2005,15:229-251.)给出的prox-类算法的计算复杂性分析表明了外梯度算法在满足单调Lipschitz-连续时具有O(1/t)的收敛率;随后相关文献在一定的条件下给出了投影收缩算法、交替方向法和Douglas-Rachford法的计算复杂性分析.受到上述计算复杂性工作的启发,利用半正定单调变分不等式的基本性质和柯西施瓦兹不等式,在一定的假设条件下,给出了半正定单调变分不等式CPC算法O(1/t)收敛率的证明.
The Correction Projection and Contraction Method（CPC Method） can solve a kind of semidefinite monotone variational inequalities without the manifestation expression of function by only computing the function value at the iteration point.Recently,A.Nemirovski（SIAM J Optim,2005,15：229-251.） proposed the efficiency estimate of prox-type method,and his analysis indicates that the extragradient method has O（1/t） convergence rate for variational inequalities with Lipschitz continuous monotone operators.Subsequently,B.S.He and X.M.Yuan give out the complexity of the projection and contraction method,the alternating direction method as well as the Douglas-Rachford operator splitting method under some appropriate conditions.Inspired by the encouraging achievement in estimating convergence rate,we establish that the CPC method has O（1/t） convergence rate for semidefinite monotone variational inequality under some suitable conditions by adopting the basic properties of semidefinite monotone variational inequalities and Cauchy Schwarz inequality in this paper.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第2期209-213,共5页
Journal of Sichuan Normal University（Natural Science）
基金
国家科技支撑计划(2011BAH24B06)资助项目
中国民航飞行学院科研基金(J2010-45)
关键词
半正定变分不等式问题
CPC算法
收敛率
semidefinite monotone variational inequality
correction projection and contraction method
convergence rate
