MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Interactions between discrete and continuous optimization and critical point theory via multi-way Lovász extensions

Jürgen Jost and Dong Zhang


We introduce and systematically study general discrete-to-continuous extensions, with several applications for combinatorial problems and discrete mathematics. This provides new perspectives for understanding relations and interactions between discrete and continuous worlds via multi-way extensions.

Lovász extension, submodularity, Combinatorial Optimization, discrete Morse theory, Lusternik-Schnirelman theory, Cheeger inequalities & isoperimetric problems, chromatic number

Related publications

2024 Journal Open Access
Jürgen Jost and Dong Zhang

Discrete-to-continuous extensions : Lovász extension and Morse theory

In: Discrete and computational geometry, 72 (2024) 1, pp. 49-72