黎曼流形上的强测地预不变凸性和强不变η-单调性及其应用
Strongly geodesic preinvexity and Strongly Invariant η-Monotonicity on Riemannian Manifolds and its Application
摘要：
本文给出了黎曼流形（RM）上的强测地预不变凸和RM上的m阶强η-不变凸.进一步，我们定义了RM上m阶强不变η-单调性.在条件C下，研究了这些函数的一个重要特征.我们构造了几个非平凡的例子来支持这些定义。其次，给出了MOP的m阶严格η-极小元（η-极小元）的一个重要而有意义的刻画，并给出了变分似不等式问题（VVLIP）的一个解.
英文摘要：
In this paper, we present strongly geodesic preinvexity on Riemannian manifolds (RM) and strongly η-invexity of order m on RM. Furthermore, we define strongly invariant η-monotonicity of order m on RM. Under Condition C, an important characterization of these functions are studied. We construct several non-trivial examples in support of these definitions. Afterwords, an important and significant characterization of a strict η-minimizers (η-minimizers)of order m for MOP and a solution to the variational like-inequality problem (VVLIP) has been derived.
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