在许多实际问题中，理想的确切"数据"和可利用的试验"数据"间不可避免地有误差，所以研究系统"数据"经扰动后一些重要性质有稳定性在理论和应用上都是必要和有意义的。误差界是优化中的重要性质，而锥不等式包含优化中许多常见的约束系统，本项目将使用变分分析方法研究数据经扰动后锥不等式误差界的稳定性。我们也将研究目标函数经线性扰动后的Holder tilt-stabilty和Holder强稳定极小值点，并考虑它们与目标函数次微分映射Holder强度量正则性之间的关系。相对于被广泛研究的局部误差界，优化问题算法的收敛分析更需要约束系统的整体误差界，本项目将研究广义方程的整体误差界；因逐段线性映射常常出现在实际问题的建模中并被用来逼近一般的非线性映射，我们将重点研究由非凸逐段线性映射所确定的广义方程的整体误差界，并应用于逐段线性向量优化问题的weak sharp minima。

The proposed project mainly studies perturbation analysis in optimization and variational analysis. We will consider conic inequalities and more general generalized equations, which contain most of constaint systems in optimization. Using variational analysis technique and in terms of subdifferential, we will study the issue of the stability of error bounds for conic inequalities when data are perturbed. We will also study the Holder tilt-stabilty and Holder strong stable minimizer related to linear perturbations of the concerned function and attempt to establish relationship between them and the strong metric regularity of the subdifferntial mapping of the concerned function. Our another aim is to study the global error bounds for generalized equations and we will focus on piecewise linear generalized equations.