supremum and infimum - Why is the lagrange dual function concave
By A Mystery Man Writer
Description
In a book I'm reading (Convex Optimization by Boyd and Vandenberghe) it says
I'm struggling to understand the last sentence. Why can one conclude concavity from having a pointwise infimum of a fam
![supremum and infimum - Why is the lagrange dual function concave](https://avishek.net/assets/images/concave-function.png)
Total Internal Reflection : Musings on Machine Learning
![supremum and infimum - Why is the lagrange dual function concave](https://image.slidesharecdn.com/realandconvexanalysis-130328021505-phpapp01/85/real-and-convex-analysis-1-320.jpg?cb=1669285210)
Real and convex analysis
![supremum and infimum - Why is the lagrange dual function concave](https://avishek.net/assets/images/affine-set.png)
Total Internal Reflection : Musings on Machine Learning
![supremum and infimum - Why is the lagrange dual function concave](https://image.slidesharecdn.com/realandconvexanalysis-130328021505-phpapp01/85/real-and-convex-analysis-2-320.jpg?cb=1669285210)
Real and convex analysis
![supremum and infimum - Why is the lagrange dual function concave](https://i.stack.imgur.com/EsmFlm.png)
convex optimization - Pointwise infimum of affine functions is
![supremum and infimum - Why is the lagrange dual function concave](https://media.springernature.com/m685/springer-static/image/art%3A10.1007%2Fs11075-021-01069-x/MediaObjects/11075_2021_1069_Fig4_HTML.png)
A first-order inexact primal-dual algorithm for a class of convex
![supremum and infimum - Why is the lagrange dual function concave](https://i1.rgstatic.net/publication/349959484_Optimal_investment_problem_under_behavioral_setting_A_Lagrange_duality_perspective/links/6167171825be2600ace20253/largepreview.png)
PDF) Optimal investment problem under behavioral setting: A
![supremum and infimum - Why is the lagrange dual function concave](https://www.researchgate.net/publication/7852826/figure/fig6/AS:667679866232848@1536198693563/Bound-is-computed-as-a-lower-bound-of-inf-f-g.png)
Bound is computed as a lower bound of inf f ; g.
![supremum and infimum - Why is the lagrange dual function concave](https://avishek.net/assets/images/convex-function.png)
Total Internal Reflection : Musings on Machine Learning
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