Abstract
where p and q represent the state and decision vectors, respectively, T represents the transformation of the process, and f(p) represents the optimal return function with initial state p. Dynamic programming is an approach to optimization. The function equation (1) is the key to a possible success in solving optimization problems through dynamic programming (e.g., see [2-5, lo]). Once a pertinent functional equation (1) of an optimization problem is formulated, an algorithm for obtaining the computational solution of the problem will be available. The functional equation approach is not only applicable to a wide range of optimization problems 12-5, 101 but also is handy in establishing inequalities 11, 8, 9, 12, 131. In 1967, Redheffer [ 111 established a general inequality (see below) base upon the idea of the following recurrent inequality:
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