Say for example we need to minimize $x_2$ subject to $x_1^2+x_2^2-1=0$ starting at $x_1=x_2=1/2$ and using $B=\nabla^2[x_2+\lambda(x_1^2+x_2^2-1)]$ with $\lambda=1$.
Now, the WHP-SQP algorithm goes like this,
Choose an initial point $x_0$ and an initial matrix $B_0$
Repeat for $k=0,1,2,...$: Obtain $p_k$ and $\lambda_{k+1}$ by solving the QP subproblem Minimize $\frac{1}{2}p^TB_kp+\nabla F(x_k)^Tp$ subject to $c_i(x_k)+\nabla c_i(x_k)^Tp=0$ for $i=1,...,l$.
Obtain a new point $x_{k+1}=x_k+sp_k$ via a line search.
Obtain $B_{k+1}$ by a quasi-Newton update of $B_k$ until $T(x_{k+1},\lambda_{k+1})<\epsilon$.
Here $T(x,\lambda)=||\nabla F(x)-\sum\lambda_i\nabla c_i(x)||+\kappa||c_i(x)||$ where $\kappa$ is a positive weighting parameter, but I'm not too concerned with computing this last part
I just need an example of one iteration of how this algorithm works
Also, here $F(x)=x_2$ and $c_1(x)=x_1^2+x_2^2-1$