Sequential Extremal Principle: Refinements and Applications
Abstract
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 (GSα) 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.
Related
- Extremal permutations of ℤn with many good slopes and applications to quantum Latin squares
- Vertex-colored Turán theorems with applications in extremal hypergraph problems
- A Self-Coupling Gaussian Extremal Inequality for Information-Constrained Optimal Transport with Applications to Rate-Distortion-Perception
- A duality principle for the neighbourhood of manifolds and applications to counting rational points near curves
- Applications of sequential spaces to Smyth power spaces and sober spaces
BibTeX
@misc{cuong2026sequential,
title = {{Sequential Extremal Principle: Refinements and Applications}},
author = {Nguyen Duy Cuong and Alexander Kruger and Nguyen Hieu Thao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11232},
eprint = {2609.11232},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11232},
}
RIS
TY - UNPB
TI - Sequential Extremal Principle: Refinements and Applications
AU - Nguyen Duy Cuong
AU - Alexander Kruger
AU - Nguyen Hieu Thao
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11232
UR - https://arxiv.org/abs/2609.11232
AB - 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.
ER -