凸优化课程

$$\mathcal{C} \text{ is convex if } \forall x,y \in \mathcal{C}, \lambda \in [0,1]: \lambda x + (1-\lambda)y \in \mathcal{C}$$

$$f(\lambda x + (1-\lambda)y) \leq \lambda f(x) + (1-\lambda)f(y)$$

$$x^{(k+1)} = x^{(k)} - \alpha_k \nabla f(x^{(k)})$$

$$x^{(k+1)} = x^{(k)} - [\nabla^2 f(x^{(k)})]^{-1} \nabla f(x^{(k)})$$

$$L(x,\lambda,\nu) = f(x) + \sum_i \lambda_i g_i(x) + \sum_j \nu_j h_j(x)$$