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.
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Notes
- 1.
J. von Neumann, “Zur Theorie der Gesellschaftsspiele”, Math. Ann. 100 (1928) 295–320.
References
W. Krabs, Optimierung und Approximation (Teubner, Stuttgart, 1975).
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Jahn, J. (2020). Duality. In: Introduction to the Theory of Nonlinear Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-42760-3_6
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DOI: https://doi.org/10.1007/978-3-030-42760-3_6
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