Duality

Abstract

The duality theory is also an additional important part of the optimization theory. A main question which is investigated in duality theory reads as follows: Under which assumptions is it possible to associate an equivalent maximization problem to a given (in general convex) minimization problem. This maximization problem is also called the optimization problem dual to the minimization problem. In this chapter we formulate the dual problem to a constrained minimization problem and we investigate the relationships between the both optimization problems. For a linear problem we transform the dual problem in such a way that we again obtain a linear optimization problem. Finally, we apply these results to a problem of linear Chebyshev approximation.