Abstract
• Why. The aim of this chapter is to teach by means of some additional examples the craft of making a complete analysis of a convex optimization problem. These examples will illustrate all theoretical concepts and results in this book. This phenomenon is in the spirit of the quote by Cervantes. Enjoy watching the frying of eggs in this chapter and then fry some eggs yourself!
• What. In this chapter, the following problems are solved completely; in brackets the technique that they illustrate is indicated.
– Least squares (convex Fermat).
– Generalized Fermat-Weber location problem (convex Fermat).
– RAS method (KKT).
– How to take a penalty (minimax and saddle point).
– Ladies Diary problem (duality theory).
– Second welfare theorem (KKT).
– Minkowski’s theorem on an enumeration of convex polytopes (KKT).
– Duality for LP (duality theory).
– Solving LP by taking a limit (the interior point algorithms are based on convex analysis).
Al freír de los huevos lo verá.
You will see it when you fry the eggs.
Miguel de Cervantes, Don Quixote (1615)
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Brinkhuis, J. (2020). Application to Convex Problems. In: Convex Analysis for Optimization. Graduate Texts in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-030-41804-5_9
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DOI: https://doi.org/10.1007/978-3-030-41804-5_9
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