论文标题
参数化的广义方程与最佳价值函数应用的巧合点
Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions
论文作者
论文摘要
本文研究参数化集值映射（多函数）的巧合点，该构图提供了一个扩展的框架，涵盖了变异分析和优化中的几个重要主题，包括参数化方程的解决方案的存在，隐式函数和固定点定理中的固定值，以及使用参数的优化等级的良好形式分析等各种变化的机器的最佳形式分析，并具有多样化的形式分析。多功能的属性，我们建立了一个一般定理，以确保存在参数依赖性的重合点映射，并具有明确的误差界限，用于无限维空间之间的参数化多功能。获得的主要结果得出了一个新的隐式函数定理，并使我们能够为与参数最小化问题相关的最佳价值函数的半持续性和连续性得出有效条件，但受参数性通用方程约束的约束。
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of solutions of parameterized generalized equations, implicit function and fixed-point theorems, optimal value functions in parametric optimization, etc. Using the advanced machinery of variational analysis and generalized differentiation that furnishes complete characterizations of well-posedness properties of multifunctions, we establish a general theorem ensuring the existence of parameter-dependent coincidence point mappings with explicit error bounds for parameterized multifunctions between infinite-dimensional spaces. The obtained major result yields a new implicit function theorem and allows us to derive efficient conditions for semicontinuity and continuity of optimal value functions associated with parametric minimization problems subject to constraints governed by parameterized generalized equations.
