Let $x_1,\ldots,x_n \in \mathbb R^d$ and $y_1,\ldots,y_n \in \{\pm 1\}$, and $\epsilon, h \gt 0$. Define $\theta(t) := Q((t-\epsilon)/h)$, where $Q(z) := 1 - \Phi(z) = \int_{z}^\infty \phi(z)\mathrm{d}z$ is the Gaussian survival function. For any  $w \in \mathbb R^d$, define

$$
L(w) := \frac{1}{n}\sum_{i=1}^n \theta(y_i f_w(x_i)),
$$

where $f_w(x) := x^\top w$, a linear function.

**Question.** Is there a convergence gradient-type scheme which can be used to optimize $L$ over the unit-sphere in $\mathbb R^d$ ?