Generalized weak sharp minima and the existence of strong Lagrangian multipliers in conic convex optimization
Generalized weak sharp minima and the existence of strong Lagrangian multipliers in conic convex optimization
复制标题
圆锥凸优化中广义弱锐极小值与强拉格朗日乘子的存在性
DOI：
--
复制
发表时间：
2016
影响因子：
1.1
通讯作者：
Jen-Chih Yao
中科院分区：
文献类型：
--
作者：
Honglin Luo;Jianwen Peng;Jen-Chih Yao
广义弱锐极小值是弱的推广。锐利的最小值，在某种意义上，它作为一个有用的工具，用于转换。对一些允许起动的不可行算法进行了演化分析。一些迭代点和不可行的点进行了优化求解。具有显式约束的运动问题。在本文中，我们进一步挖掘。圆锥凸上广义弱锐极小值的刻画。优化（简称CCP）。新概念，I型广义尖锐。引入了一类广义弱锐极小值和一类广义弱锐极小值。用于研究拉格朗日乘数存在性的CCP。约束qualications。so-的标准和特征。CCP的解集为I型广义弱锐极小集。给出了。我们表明这两个概念与but密切相关。比拉格朗日多钳存在的条件强得多。作为应用，局部误差界适用于一类非退化。研究了二次微分凸包含问题。
Generalized weak sharp minima is an extension of weak.sharp minima in the sense that it serves as a useful tool for conver-.gence analysis of some infeasible algorithms which permit the starting.point and some iteration points to be infeasible to solve the optimiza-.tion problems with explicit constraints. In this paper, we further tap.the characterizations of generalized weak sharp minima in conic convex.optimization (CCP for short). New concepts, type I generalized sharp.minimum and type I generalized weak sharp minima, are introduced in.CCP for studying the existence of Lagrangian multipliers without any.constraint qualications. Both criteria and characterizations for the so-.lution set of CCP to be the set of type I generalized weak sharp minima.are given. We show that these two concepts are closely related to but.much stronger than the conditions of the existence of Lagrangian multi-.pliers. As applications, local error bounds for a class of non-degenerate.conic dierential convex inclusion problems are studied.