Global optimization: On pathlengths in min-max graphs (Q5928206)

This research paper is devoted to path lengths in Min-Max graphs for some kinds of global optimization problems, starting from pertinent previous results of the authors and being based on the following main result: For every smooth, compact and connected \(n\)-manifold \(X\) without boundary, \(x,y\in X\) arbitrary different points and \(k\in N^*\), there exists a smooth nondegenerate real function \(f\) defined on \(X\) such that \(x,y\) are local minima of \(f\), the corresponding graph to the Riemannian metric is connected and the length of the shortest path in this graph between \(x\) end \(y\) exceeds \(k\).