Eigenvalue Problem and Non linear Programming Problem: For Economic Studies

Students of economics are well aware that there is a close relationship between nonlinear programming and dynamic theory. Linear programming is insufficient for analyzing the complex dynamics of real economies, and the use of a nonlinear dynamic model is essential. In this publication, therefore, systematically summarizing nonlinear programming problems is the main subject. These have various economic applications. A secondary topic is Frobenius’s theorem related to nonlinear transformation. This is grounded in the fact that Frobenius roots in nonlinear transformations can be characterized as upper limits on real numbers that bring about non-negative solutions to nonlinear inequalities and that Frobenius’s theorem gives us useful information when trying to solve stability problems. 

In this book, while trying to apply them to economic theory as much as possible, I have attempted to describe them systematically and self-contained to the fullest extent possible and summarize my modest research results until now in this area. 

In this publication, I have made significant additions and revisions to the book entitled “Nonlinear Programming and Nonlinear Programming Eigenvalue Problems,” which was published in September 1995 as a research work in the Chukyo University Economics Research Book Series No. 5, by Keiso Shobo. There are several reasons for this first new publication in 20 years: nonlinear models are still relevant as a tool in economic issues today, and many areas of the original text required revision. In this publication, I have changed the title somewhat from the Japanese version to “Eigenvalue Problem and Nonlinear Programming Problem.”