definition of the convex optimization

发布时间 2023-10-18 10:46:29作者: zzqDeco

A convex optimization problem is one in which the objective and constraint functions are convex, which means they satisfy the inequality

\(f_i(\alpha x+\beta y) \leq \alpha f_i(x)+\beta f_i(y)\)

for all \(x, y \in \mathbf{R}^n\) and all \(\alpha, \beta \in \mathbf{R}\) with \(\alpha+\beta=1, \alpha \geq 0, \beta \geq 0\).

Since any linear program is therefore a convex optimization problem, we can consider convex optimization to be a generalization of linear programming.