Eigenvalue Problem and Nonlinear Programming Problem For Economic Studies

This book focuses on the Frobenius theorem regarding a nonlinear simultaneous system. The Frobenius theorem is well known as a condition for a linear simultaneous system’s having a nonnegative solution. Generally, however, the condition of a simultaneous system, including a non-linear system’s having a nonnegative solution, is hardly discussed at all. This book, therefore, extends the conventional Frobenius theorem for nonlinear simultaneous systems for economic analysis.

 Almost all static optimization problems in economics involve nonlinear programing. Theoretical models in economics are described in the form of a simultaneous system resulting from the rational optimization behavior of households and enterprises. On the other hand, rational optimization behavior of households and enterprises is, mathematically speaking, expressed as nonlinear programing. For this reason it is important to understand the meaning of nonlinear programing. Because this book includes explanations of the relations among various restrictions in a nonlinear programing systematically and clearly, this book is suitable for students in graduate school programs in economics.

Chapter 1   Nonlinear Programming.- Chapter 2   Perron-Frobenius Theorem.- Chapter 3   Dominant Diagonal Matrix and Quadratic Form.- Chapter 4   Recent Issue on Eigenvalue Problem.- Appendix   Lists of Mathematical Theorems and Definitions.

Keiko Nakayama, Professor, Chukyo University, Nagoya, Japan

Keiko Nakayama, 2022, A Forest Environmental Tax Scheme in Japan: Toward Water Source Cultivation-, Springer

Keiko Nakayama and Yuzuru Miyata (Editors), 2019, Theoretical and Empirical Analysis in Environmental Economics, Springer (Chapter 1 and Chapter 4)