This post aims at providing some intuition into cone programs from different perspectives; in particular:
- Equivalence of different formulations of cone programs
- Fenchel duality
- Primal-dual optimality conditions (OC)
- OCs as variational inequalities
- Homogeneous self-dual embeddings (HSDEs)
- OCs for HSDEs
The gradient method with constant step length is the simplest method for solving unconstrained optimisation problems involving a continuously differentiable function with Lipschitz-continuous gradient. The motivation for this post came after reading this Wikipedia article where it is stated that under certain assumptions the sequence converges to a local optimum, but it is no further discussion is provided. Continue reading →
Where here we discover some interesting facts about continuous convex functions.
We know that a function is convex if
for all and .
We see that if is a continuous function, then an equivalent condition for convexity is that either of the following inequalities holds