From dynamic programming to bynamic programming (Q1260896)

The author suggests a new sequential optimization method called `bynamic programming', which includes dynamic programming as a special case. The objective function \(g(x,.)\) defined on \(X\times R^{\ell}\) is separable and at the same time nonincreasing or nondecreasing in the second variable for \(x\in X^ -\), \(x\in X^ +\) respectively, where \(X\) is the disjoint union of \(X^ +\) and \(X^ -\), the so called bitonicity property. A theoretical background of bynamic programming is given. Multiplicative programming and multiplicatively additive programming are presented as special cases of bynamic programming. Infinite horizon bynamic programming is studied in the concluding part of the paper.