Definition Standard form convex optimization problem [lcc-001G]

A convex optimization problem in standard form consists of

1. A convex function f_0: \mathbb {R}^k \to \mathbb {R}
2. A list of convex functions f_1, \dots f_n: \mathbb {R}^k \to \mathbb {R}
3. A list of affine functions g_1,\dots g_m: \mathbb {R}^k \to \mathbb {R}

The problem then is to find x \in \mathbb {R}^k which minimizes f_0(x) subject to the constraints f_i(x) \leq 0, g_i(x)=0