Correction

This article refers to:

A decentralized coordination algorithm for multi-objective linear programming with block angular structure

Article title: A decentralized coordination algorithm for multi-objective linear programming with block angular structure

Authors: Okpoti, E. S. & Jeong, I. J.

Journal: Engineering Optimization

DOI: http://dx.doi.org/10.1080/0305215X.2019.1698035

When the above article was first published online, the illustrative example in Section 5.1 did not match with the theory and might have confused the readers. Hence, the whole section has been amended.

In addition, several equations and notations were incorrect. These are as follows:

Section 3.1:

– In Algorithm Phase I, “$|{\mathit{x}}_{\mathit{i}}^{\mathit{t}}-{\mathit{\epsilon }}_{\mathit{i}}^{\mathit{t}}|$” and “$|{\mathit{x}}_{\mathit{i}}^{\mathit{t}+\mathbf{\text{1}}}-{\mathit{\epsilon }}_{\mathit{i}}^{\mathit{t}+\mathbf{\text{1}}}|$” should be in double vertical bar.

– In Algorithm Phase II, the square symbol in “$|{\mathit{x}}_{\mathit{i}}^{\mathit{k}+\mathbf{\text{1}}}-{\mathit{x}}_{\mathit{c}}^{\mathit{k}\mathbf{\text{2}}}|$” should be deleted.

– In the equation “$\underset{x_i,x_c}{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{z}\mathrm{e}}{f}_1\left(x_i\right)+\frac{\rho }{2}\parallel x_i-x_i^{0\ast }{\parallel }^2$”, “$f_1$” should be “$f_i$”.

– In Algorithm Phase I, “$x_i^{0\ast }$” is missing in the statement “$\mathit{H}$ be a set containing”.

Section 4.1:

– The squared symbol in “$\parallel \cdot {\parallel }^2$” should be deleted.

Section 4.2:

– The squared symbols for the lambda calculations on Equation 12 should be deleted.

– The squared symbol on Equation 15 should be deleted.

Moreover, in Figures 1 and 2, the subscript of the phi symbol in “Agent m” should be “m” and Figures 3 and 4 have been replaced with new versions for better presentation.

These have been corrected for both online and print versions.