Rainer E . Perspective of Monge properties

Perspectives of Monge Properties in Optimization

Existence and multiplicity of positive solutions for singular‎ ‎Monge-Amp‎‎$‎rmgrave{e}‎$re system

Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

On the Traveling Salesman Problem with a Relaxed Monge Matrix

We show that the traveling salesman problem with a symmetric relaxed Monge matrix as distance matrix is pyramidally solvable and can thus be solved by dynamic programming. Furthermore, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix becomes a relaxed Monge matrix.

Optimierung Und Kontrolle Projektbereich Diskrete Optimierung on the Tsp with a Relaxed General Distribution Matrix on the Traveling Salesman Problem with a Relaxed Monge Matrix

We show that the traveling salesman problem with a symmetric relaxed Monge matrix as distance matrix is pyramidally solvable and can thus be solved by dynamic programming. Furthermore, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix becomes a relaxed Monge matrix.

The Quadratic Assignment Problem with a Monotone Anti-Monge and a Symmetric Toeplitz Matrix: Easy and Hard Cases

This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other coefficient matrix is a symmetric Toeplitz matrix. This restricted version is called the Anti-Monge–Toeplitz QAP. There are three well-known combinatorial problems that can be modeled via the Anti...