Linear Programming Using MATLAB® pp E1-E3 | Cite as

# Correction to: Linear Programming Using MATLAB^{®}

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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.