supremum and infimum - Why is the lagrange dual function concave

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

All Lagrangian Duals (of Minimizations) are Concave

definition - How is a convex function defined when the domain is a

optimization - Minimizing linear least squares using Lagrangian $L

5. Duality

Convex Optimization Without the Agonizing Pain

Evenly Quasiconvex Functions

PDF) Convex Inequalities and Functional Space with the Convex Semi

A difference-of-convex functions approach for sparse PDE optimal

PDF) Optimal investment problem under behavioral setting: A

Ridge regression as a constrained optimization - JLD STATS

What is the definition of a convex function in optimization? What

real analysis - The dual function g is concave, even when the

Real and convex analysis

Total Internal Reflection : Musings on Machine Learning

Convex Optimization Theory