Correction: Latest developments in node-based shape optimization using Vertex Morphing parameterization

Correction to: Structural and Multidisciplinary Optimization (2022) 65:198 https://doi.org/10.1007/s00158-022-03279-w

In the original publication of the article, the author would like to update the following changes in the equations

1. After Eq. 18, the changes in bold (“where $\varvec{y}^{(i)}=\nabla f(\varvec{x}^{(i-1)})-\nabla f(\varvec{x}^{(i)})$”) to new (“where $\varvec{y}^{(i)}=\nabla f(\varvec{x}^{(i)})-\nabla f(\varvec{x}^{(i-1)})$”);

2. Adding the missing equation between Eqs. 20–22. The addition of equation in bold:

$$\varvec{H}^{(i)} = [\alpha_{k}^{(i)}] \\$$

(20)

$$\alpha_{k}^{(i)} = \min \left( abs \left [\frac{{\varvec{y}}^{(i),T}_k {\varvec{d}}_{k}^{(i-1)}} {{\varvec{y}}_{k}^{(i),T} {\varvec{y}}_{k}^{(i)}} \right], \alpha_{k, max}^{(i)} \right)$$

(21)

$${\varvec{y}}_{k}^{(i)} = {\varvec{s}}_k^{(i-1)} - {\varvec{s}}_{k}^{(i)}$$

(22)

$$\Delta \varvec{x}^{(i)} = \varvec{H}^{(i)} \cdot \varvec{s}^{(i)}$$

(23)

3. In Chapter 4.3, in the enumerated list, part 3(b). We need to change the reference to the equation: old 20, new 23. The changes in bold

new (Compute shape update $\Delta \varvec{x}^{(i)}$, Eq. (23)”).

Now, the original article has been updated.