发表机构
Faculty of Mathematics, College of Natural Sciences Can Tho University; School of Science, Engineering and Technology RMIT University Vietnam; Analytical and Algebraic Methods in Optimization Research Group Faculty of Mathematics and Statistics Ton Duc Thang University（越南芹苴大学自然科学学院数学系; 越南皇家墨尔本理工学院科学与工程与技术学院; 越南胡志明市统一大学数学与统计学院优化分析代数方法研究组）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究序贯极值原理，给出固定平移序列下极值性与平稳性的精确刻画，证明其稳定性，建立对偶必要条件，并应用于最小值未必可达的约束优化问题。
AI 中文摘要
本文讨论了序贯极值性和平稳性性质，重点研究了与固定平移序列相对应的性质。文中给出了这些性质的精确定量刻画。我们特别证明了序贯（以及传统）极值性和近似平稳性性质具有某种稳定性，而（非近似的）平稳性则不具备这种稳定性。针对固定和非固定平移序列，建立了序贯极值性和平稳性性质的对偶必要条件。文中还提出了序贯扩展极值原理的一个版本。在陈述中，我们采用了某些广义分离条件$(GS)$和$(GS_\alpha)$以及一个互补的原-对偶条件$(PD)$。为了说明该模型，我们证明了一个约束最小化问题的对偶最优性/平稳性条件，在该问题中最小值不一定能达到。
英文摘要
Sequential extremality and stationarity properties are discussed with the emphasis on those corresponding to fixed sequences of translations. Exact quantitative characterisations of the properties are provided. We show, in particular, that the sequential (as well as conventional) extremality and approximate stationarity properties possess certain stability, while the (non-approximate) stationarity does not. Dual necessary conditions for the sequential extremality and stationarity properties with fixed and non-fixed sequences of translations are established. A version of the sequential extended extremal principle is formulated. In the statements, we employ certain generalised separation conditions $(GS)$ and $(GS_α)$ as well as a complementary primal-dual condition $(PD)$. To illustrate the model, we prove dual optimality/stationarity conditions for a constrained minimisation problem in which the minimal value is not necessarily attained.
Comments25 pages
