On the Dini-Hadamard subdifferential of the difference of two functions

通过Busemann函数的亚微分特征化及其在Hadamard流形上的DC优化应用

A subdifferential characterization via Busemann functions and applications to DC optimization on Hadamard manifolds

本文提出基于Busemann函数的亚微分特征化方法，用于Hadamard流形上的差分凸优化，通过凹性设计优化算法并分析其收敛性。

拓扑向量空间中Dini导数的乘子规则

Multiplier rules for Dini-derivatives in a topological vector space

本文在拓扑向量空间和Banach空间中，将最优性条件从Fréchet、Gateaux可微及Clarke次微分情形推广到Dini可微函数，并扩展了Pourciau的凸性结果至Dini-伪凸性。

子微分理论与通过Busemann函数的Fenchel共轭在Hadamard流形上

Busemann-coupling subdifferentials and Fenchel biconjugation on Hadamard manifolds

本文通过Busemann函数定义子微分，研究Fenchel-Young不等式成立条件及非平凡仿射函数的存在性，揭示了凸分析中的对偶原理和里奇曲率对刚性结论的必要性。

Minimal convex majorants of functions and Demyanov--Rubinov super(sub)differentials

The primary goal of the paper is to establish characteristic properties of (extended) real-valued functions defined on normed vector spaces that admit the representation as the lower envelope of their minimal (with respect to pointwise ordering) convex majorants. The results presented in the paper generalize and extend the well-known Demyanov-Rubinov characterization of upper semicontinuous positively homogeneous functions as the lower envelope of exhaustive families of continuous sublinear functions to more larger classes of (not necessarily positively homogeneous) functions defined on arbitr…

Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces

We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. Firstly, we provide an upper estimate of its Dini--Hadamard subdifferential in terms of the Clarke subdifferential of the Lipschitz continuous integrand and the Clarke normal cone to the graph of the set-valued mapping describing dynamics. Secondly, we derive a necessary condition for optimality in the form of an adjoint inclusion that grasps a connection between the Euler--Lagrange condition and the maximum principle.

一种基于Busemann函数的混合投影-近点算法用于Hadamard流形上的优化问题

A Busemann hybrid projection-proximal point algorithm for optimization problems on Hadamard manifolds

本文提出了一种基于Busemann函数的混合投影-近点算法，用于Hadamard流形上的优化问题，实现了几何内禀的迭代方案并证明了全局收敛性。