Complex Convexity

E. Lieb convexity inequalities and noncommutaive Bernstein inequality in Jordan-algebraic setting

We describe a Jordan-algebraic version of E. Lieb convexity inequalities. A joint convexity of Jordan-algebraic version of quantum entropy is proven. A version of noncommutative Bernstein inequality is proven as an application of one of convexity inequalities. A spectral theory on semi-simple complex algebras is used as a tool to prove the convexity results. Possible applications to optimizatio...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Calculating Cost Efficiency with Integer Data in the Absence of Convexity

One of the new topics in DEA is the data with integer values. In DEA classic models, it is assumed that input and output variables have real values. However, in many cases, some inputs or outputs can have integer values. Measuring cost efficiency is another method to evaluate the performance and assess the capabilities of a single decision-making unit for manufacturing current products at a min...

Convexity in complex networks

Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes i...

C-convexity in Infinite-dimensional Banach Spaces and Applications to Kergin Interpolation

We investigate the concepts of linear convexity and C-convexity in complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space X and a point p / ∈Ω, there is a complex hyperplane through p that does not intersect Ω. We also prov...