Duality

Johannes Jahn
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Johannes Jahn: Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik

Chapter Chapter 6 in Introduction to the Theory of Nonlinear Optimization, 1996, pp 163-189 from Springer

Abstract: 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.

Keywords: Saddle Point; Dual Problem; Duality Theory; Primal Problem; Duality Theorem (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-3-662-03271-8_6

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