2 votes
Accepted

Applying Riesz Representation Theorem to show existence of dual basis

Let $v_n$ be a collection of vectors in a Hilbert space $\mathcal{H},$ such that the linear span is dense and $$\|(a_k)\|_{\ell^2}\sim \left \|\sum a_kv_k\right \|\qquad (*)$$ Consider the functional $...
user avatar
1 vote
Accepted

Dual of a simple constrained least-squares problem

The lagrange function that you wrote is slightly incorrect. You have to exchange $b^T$ and $b$. To obtain the dual that you are looking for: \begin{align} \max_{u\in \mathbb R}\min_{x\in \mathbb R^n} \...
user avatar
  • 5,549
1 vote

How is the dual problem for conic programs derived via Lagrangians?

The main idea is that we can use the relation $x\in K$ implicitly; we could penalize it directly in the Lagrangian, but we can also use the fact that $x\in K$ to derive a relation on other quantities. ...
user avatar
  • 2,400
1 vote

Relationship between minmax theorems and strong duality

Perhaps it is easiest to understand the relation of the Minimax Theorem and linear programming in the classical context of finite zero-sum two-player games. Suppose that we want to determine if player ...
user avatar
  • 15.7k

Only top scored, non community-wiki answers of a minimum length are eligible