Correction to: Linear Programming Using MATLAB^®

The original version of the book was inadvertently published without updating the following corrections:

Preface:

On page ix, the last line reads:

April 2017

It should read:

November 2017

Chapter 1:

On page 5, 10^th line from top reads:

A more efficient approach is the Primal-Dual Exterior Point Simplex Algorithm (PDEPSA) proposed by Samaras [23] and Paparrizos [22].

It should read:

A more efficient approach is the Primal-Dual Exterior Point Simplex Algorithm (PDEPSA) proposed by Samaras [23] and Paparrizos et al. [22].

Chapter 2:

On page 68, alignment of the following equations in Table 2.8 were as follows:

s ₀ = ∑ _{j ∈ P} λ _j s _j

and the direction

d _B = −∑ _{j ∈ P} λ _j h _j, where h _j = A _B ⁻¹ A _. j.

It should be as follows:

s ₀ = ∑ _{j ∈ P} λ _j s _j

and the direction

d _B = −∑ _{j ∈ P} λ _j h _j, where h _j = A _B ⁻¹ A _. j.

And

if d _B ≥ 0 then

if s ₀ = 0 then STOP. The LP problem is optimal.

else

choose the leaving variable x _B[r] = x _k using the following relation:

$a = \frac{x_{B[r]}} {-d_{B[r]}} =\min \left \{ \frac{x_{B[i]}} {-d_{B[i]}}: d_{B[i]} < 0\right \},i = 1,2,\cdots \,,m$

if a = ∞, the LP problem is unbounded.

It should be as follows:

if d _B ≥ 0 then

if s ₀ = 0 then STOP. The LP problem is optimal.

else

choose the leaving variable x _B[r] = x _k using the following relation:

$a = \frac{x_{B[r]}} {-d_{B[r]}} =\min \left \{ \frac{x_{B[i]}} {-d_{B[i]}}: d_{B[i]} < 0\right \},i = 1,2,\cdots \,,m$

if a = ∞, the LP problem is unbounded.

Chapter 4:

On page 211, 15^th line from top, the sentence reads:

The column “Total size reduction” in Table 4.2 is calculated as follows: − (m _new + n _new − m − n)∕((m + n).

It should read:

The column “Total size reduction” in Table 4.2 is calculated as follows: − (m _new + n _new − m − n)∕(m + n).

Chapter 8:

On page 345, 7^th line from bottom, the sentence reads:

There are elements in vector h ₁ that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that h _i l ≤ 0, therefore $\frac{x_{B[i]}} {h_{il}}$ is not defined):

It should read:

There are elements in vector h ₁ that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that h _il ≤ 0, therefore $\frac{x_{B[i]}} {h_{il}}$ is not defined):

Chapter 10:

On page 439, alignment of the following equation in Table 10.1 was as follows:

s ₀ = ∑ _{j ∈ P} λ _j s _j

and the direction

$d_{B} = -\sum _{j\in P}\lambda _{j}h_{j}$, where $h_{j} = A_{B}^{-1}A_{.j}$.

Step 2.1. (Test of Optimality).

if P = ∅ then STOP. (LP.1) is optimal.

else

if d _B ≥ 0 then

if s ₀ = 0 then STOP. (LP.1) is optimal.

It should be as follows:

s ₀ = ∑ _{j ∈ P} λ _j s _j

and the direction

d _B = −∑ _{j ∈ P} λ _j h _j, where h _j = A _B ⁻¹ A _. j.

Step 2.1. (Test of Optimality).

if P = ∅ then STOP. (LP.1) is optimal.

else

if d _B ≥ 0 then

if s ₀ = 0 then STOP. (LP.1) is optimal.