Abstract
There is a formal set of mathematical conditions that describe the minima of constrained or unconstrained optimization problems. Called the Karush-Kuhn-Tucker (KKT) conditions, they can sometimes be used to solve directly for minimum points in design space. This chapter shows a series of examples on how the KKT conditions can be used to find the minima of unconstrained and constrained optimization problems.
Each problem that I solved became a rule, which served afterwards to solve other problems
-Rene DesCartes
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References
Kuhn HW, Tucker AW (1951) Nonlinear programming, proceedings of the 2nd Berkeley symposium, p 481–492
Karush W (1939) Minima of functions of several variables with inequalities as side constraints, M. Sc. Dissertation, Dept. of Mathematics, Univ. of Chicago
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French, M. (2018). General Conditions for Solving Optimization Problems: Karush-Kuhn-Tucker Conditions. In: Fundamentals of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-76192-3_6
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DOI: https://doi.org/10.1007/978-3-319-76192-3_6
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