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Vietnam Journal of Mathematics 35:4(2007) 373-386 Admissible Transformations and Assignment Problems  Rainer E. Burkard Abstract.  We introduce the notion of admissible transformations which is related to the Hungarian method for solving assignment problems. Admissible transformations are stated for linear, quadratic and multi-index assignment problems. Their application to find good lower bounds and/or to solve the problem, respectively, is outlined. Finally it is shown that admissible transformations can also be applied to so-called algebraic objective functions whose cost elements are drawn from a totally ordered semigroup.     Keywords: Combinatorial optimization, assignment problems, quadratic assignment problem, multi-index assignment problem, admissible transformation, algebraic optimization.

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