论文标题
功能的变化凸和优化方面的差异
Variational Convexity of Functions and Variational Sufficiency in Optimization
论文作者
论文摘要
该论文致力于研究的研究，函数变异凸度的特征和应用，Rockafellar最近引入了该特性及其强大的对应物。首先，我们表明，扩展实现函数的这些变异性能分别等同于其莫罗包层的常规（局部）凸度和强凸度。然后，我们通过其二阶细分（广义Hessians）来得出一般函数的变分凸度和变异强凸度的新特征，这些函数是亚级映射的代码。我们还研究了这些概念与局部最小化和倾斜稳定的本地最小化器的关系。所获得的结果用于表征复合优化的变异和强差异相关概念，并应用于非线性编程。
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these variational properties of an extended-real-valued function are equivalent to, respectively, the conventional (local) convexity and strong convexity of its Moreau envelope. Then we derive new characterizations of both variational convexity and variational strong convexity of general functions via their second-order subdifferentials (generalized Hessians), which are coderivatives of subgradient mappings. We also study relationships of these notions with local minimizers and tilt-stable local minimizers. The obtained results are used for characterizing related notions of variational and strong variational sufficiency in composite optimization with applications to nonlinear programming.
