The main goal of this paper is to investigate the properties and connections of neatly and semistrictly quasiconvex functions, especially when they appear in constrained and unconstrained optimization problems. The lower global subdifferential, recently introduced in the literature, plays an essential role in this study. We present several optimality conditions for constrained and unconstrained nonsmooth neatly/semistrictly quasiconvex optimization problems in terms of lower global subdifferentials. To this end, for a constrained optimization problem, we present some characterizations for the normal and tangent cones and the cone of feasible directions of the feasible set. Some relationships between the Greenberg–Pierskalla, tangentially and lower global subdifferentials of neatly and semistrictly quasiconvex functions are also given. The mentioned relationships show that the outcomes of this paper generalize some results existing in the literature.

本文的主要目标是研究整齐和半严格拟凸函数的性质和联系，尤其是当它们出现在约束和无约束优化问题中时。最近在文献中引入的较低的全局亚微分在本研究中起着至关重要的作用。我们根据较低的全局微分，为受约束和不受约束的非光滑整齐/半严格拟凸优化问题提出了几个最优性条件。为此，对于约束优化问题，我们提出了法线锥和切线锥以及可行集的可行方向锥的一些特征。还给出了整齐和半严格拟凸函数的 Greenberg–Pierskalla、切向和​​下全局子微分之间的一些关系。