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33In this tutorial, we will show how to model and solve the nonconvex nonsmooth least-square problem
44``` math
5- \min_{x \in \mathbb{R}^n} \frac {1}{2} \|Ax - b\|_2^2 + \lambda \|x\|_0.
5+ \min_{x \in \mathbb{R}^n} \tfrac {1}{2} \|Ax - b\|_2^2 + \lambda \|x\|_0.
66```
77
88## Modelling the problem
99We first formulate the objective function as the sum of a smooth function $f$ and a nonsmooth regularizer $h$:
1010``` math
11- \frac {1}{2} \|Ax - b\|_2^2 + \lambda \|x\|_0 = f(x) + h(x),
11+ \tfrac {1}{2} \|Ax - b\|_2^2 + \lambda \|x\|_0 = f(x) + h(x),
1212```
1313where
1414``` math
1515\begin{align*}
16- f(x) &:= \frac {1}{2} \|Ax - b\|_2^2,\\
16+ f(x) &:= \tfrac {1}{2} \|Ax - b\|_2^2,\\
1717h(x) &:= \lambda\|x\|_0.
1818\end{align*}
1919```
Original file line number Diff line number Diff line change @@ -24,7 +24,7 @@ Next, we expect the shifted model `ψ::ShiftedFoo` to
2424
2525The proximal mapping is defined as
2626``` math
27- \text{prox}(\psi, q, \sigma) := \argmin_y \ \psi(y) + \frac {\sigma}{2} \|y - q\|_2^2.
27+ \text{prox}(\psi, q, \sigma) := \argmin_y \ \psi(y) + \tfrac {\sigma}{2} \|y - q\|_2^2.
2828```
2929
3030!!! note
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