Statistical Cluster Points and Turnpike Theorem in Nonconvex Problems

By M. A. Mamedov, Serpil Pehlivan. 2001

66 citations recorded by the source corpus.

In this paper we develop the method suggested by S. Pehlivan and M. A. Mamedov (“Statistical Cluster Points and Turnpike,” submitted), where it was proved that under some conditions optimal paths have the same unique stationary limit point–stationary cluster point. This notion was introduced by J. A. Fridy (1993, Proc. Amer. Math. Soc.118, 1187–1192) and it turns out to be a very useful and interesting tool in turnpike theory. The purpose of this paper is to avoid the convexity conditions. Here the turnpike theorem is proved under conditions that are quite different from those of Pehlivan and Mamedov and may be satisfied for the mappings with nonconvex images and for nonconcave functions in the definition of functionals.

Subfields: Geometry and Topology, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e1a99d9b2d740e40352e3010ed41bcc4b0d58419

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Güncan
2. Salih Aytar
3. M. A. Mamedov
4. Serpil Pehlivan

In Management Science and Operations Research

1. Salih Aytar
2. A. Güncan
3. Serpil Pehlivan
4. M. A. Mamedov

In Statistics and Probability

1. Salih Aytar
2. A. Güncan
3. Serpil Pehlivan
4. M. A. Mamedov

Citations in the corpus

• Rough Statistical Convergence (2008, background): “The theory of statistical convergence has been discussed in trigonometric series [19], summability theory [5], measure theory [10, 11], turnpike theory [9, 12], approximation theory [7], fuzzy set theory [1], and so forth.”
• Statistical Cluster Points of Sequences in Finite Dimensional Spaces (2004, methodology): “In [8] these concepts were used in Turnpike theory as an application.”