Another clarification on quasi-newton secant equation (yes I forgot to save it)

Author: inikishev

docs/overview/5. Quasi-Newton methods.ipynb

@@ -89,7 +89,7 @@
     "\n",
     "To understand the secant equation, consider hessian matrix $H$ and an arbitrary vector $s$. Define $y$ as hessian-vector product with vector $s$, so $Hs = y$. This is the secant equation. In quasi-newton methods $y_k = \\nabla f(x_k) - \\nabla f(x_{k-1})$ actually estimates hessian-vector product with $s_k=x_k - x_{k-1}$ through the finite difference formula (I am too lazy to write it now but it's very easy to show). And you can, indeed, use any other vector in place of $s$, provided you can compute a hessian-vector product with it.\n",
     "\n",
-    "There are many solutions to $B_{k+1} s_k = y_k$, so usually a solution is picked such that $B_{k+1}$ is as close as possible to $B_k$ in some norm. Keeping $B_{k+1}$ close to $B_k$ makes sure as little information is lost as possible. Other constraints are may be imposed as well such as keeping $B$ positive definite and symmetric.\n",
+    "There are many solutions to $B_{k+1} s_k = y_k$, so usually a solution is picked such that $B_{k+1}$ is as close as possible to $B_k$ in some norm. Keeping $B_{k+1}$ close to $B_k$ makes sure as little information from $B_k$ is lost as possible. Other constraints are may be imposed as well such as keeping $B$ positive definite and symmetric.\n",
     "\n",
     "For example, here is BFGS update for $B$:\n",
     "$$\n",