BIBO稳定性的对偶概念

A Notion of Total Dual Integrality for Convex, Semidefinite, and Extended Formulations

Total dual integrality is a powerful and unifying concept in polyhedral combinatorics and integer programming that enables the refinement of geometric min-max relations given by linear programming Strong Duality into combinatorial min-max theorems. The definition of total dual integrality (TDI) revolves around the existence of optimal dual solutions that are integral, and thus naturally applies to a host of combinatorial optimization problems that are cast as integer programs whose LP relaxations have the TDIness property. However, when combinatorial problems are formulated using more general …

Facially Dual Complete (Nice) cones and lexicographic tangents

We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the well-known and commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of faces of convex sets. Based on these new notions, we obtain a necessary condition and a sufficient condition for a cone to be facially dual complete. In our sufficient condition, we utilize a new notion calle…

广义共轭视角下非欧光滑性与强凸性的对偶性

Dualities for non-Euclidean smoothness and strong convexity under the light of generalized conjugacy

针对非欧相对光滑性与强凸性的共轭对偶性这一开放问题，本文基于广义共轭引入各向异性强凸性与光滑性作为对偶概念，证明其属于特定上下包络的超类且为真包含。

Dual and Generalized Dual Cones in Banach Spaces

The primary objective of this paper is to propose and analyze the notion of dual cones associated with the metric projection and generalized projection in Banach spaces. We show that the dual cones, related to the metric projection and generalized metric projection, lose many important properties in transitioning from Hilbert spaces to Banach spaces. We also propose and analyze the notions of faces and visions in Banach spaces and relate them to the metric projection and generalized projection. We provide many illustrative examples to give insight into the given results.

极大线性离散事件系统不变空间的对偶性

Duality between invariant spaces for max-plus linear discrete event systems

本文将条件不变空间和受控不变空间的概念推广到极大加半环或热带半环上的线性动力系统。我们建立了一个对偶定理，这两个概念，我们用来构建动态观察员。这些在某些系统系数可能在一定间隔内变化的情况下是有用的。结果示出了一个制造系统的应用程序。