Given function f:ℝd→ℝf: \mathbb{R}^d \rightarrow \mathbb{R}. Find xˆ\hat{x} such that:

f(\hat{x}) \leq \min_x f(x) + \epsilon$$ ^f11fcd --- Have some function $f: \mathbb{R}^d \rightarrow \mathbb{R}$. Want to find $x^*$ such that: $$f(x^*) = \min_x f(x^*) ParseError: Can't use function '$' in math mode at position 39: …f(x) + \epsilon$̲$ ^f11fcd --- …

Or at least xˆ\hat{x} which is close to a minimum e.g. #^f11fcd

Often have additional constraints such as 𝐱>0\mathbf{x} > 0, ||𝐱||2≤R||\mathbf{x}||_2 \leq R, ||𝐱||1≤R||\mathbf{x}||_1 \leq R, 𝐚T𝐱>c\mathbf{a}^T \mathbf{x} > c

Also see: Convex Optimization notes (specific type of continuous optimization)