誠一 岩本

Dog Chases Rabbit : An Invariant Imbedding

In this paper we solve a continuous non-optimization dynamic programming problem: Dog Chases Rabbit problem. The problem has been originated by R. Bellman. We give a complete solution through an invariant imbedding approach. Some related results are derived.

The Golden Quandratic Equations

This paper considers a sequence of quadratic equations(QEs),which are called Golden quadratic equations. The first Golden QE is a well known Fibonacci QE. We introduce a general form of Golden QE― the -th Golden quadratic equation― by solving an eigenvalue problem of2×2 integer symmetric matrices. We translate the eigenvalue problem into an equivalent optimization problem.

Maximum Altitude : An Invariant Imbedding

In this paper we solve a continuous non-optimization dynamic programming problem: Maximum Altitude problem. The problem has been originated by R. Bellman. We consider three maximum altitude problems. A complete solution through an invariant imbedding is derived. Each problem accompanies a few typical examples.