## Optimization

“ An act, process, or methodology of making something (such as a design, system, or decision) as fully perfect, functional, or effective as possible”

## Optimization

\begin{align*} \min \enspace&f(x)\\ \text{subject to: }&x \text{ is in } C\qquad \end{align*}

## Convex optimization

“ A convex function refers to a function whose graph is shaped like a cup.”

## Convex optimization

Lines between any two points are "inside" the cup.

## Convex optimization

Lines between any two points are "inside" the cup.

### Convex relaxations

Hard optimization problem $$\Downarrow$$ Easier, bigger, convex problem

## Symmetry reduction

Can we solve symmetric convex problems faster?

## Symmetry reduction

• How to find symmetries?
• How to exploit symmetries?
• Which problems can we reduce?