Correction to: Linear Programming Using MATLAB®

Correction
Part of the Springer Optimization and Its Applications book series (SOIA, volume 127)

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

Preface:

On page ix, the last line reads:

April 2017

November 2017

Chapter 1:

On page 5, 10th line from top reads:

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

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:

s0 = jPλjsj

and the direction

dB = −jPλjhj, where hj = AB−1A. j.

It should be as follows:

s0 = jPλjsj

and the direction

dB = −jPλjhj, where hj = AB−1A. j.

And

if dB ≥ 0 then

if s0 = 0 then STOP. The LP problem is optimal.

else

choose the leaving variable xB[r] = xk 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 dB ≥ 0 then

if s0 = 0 then STOP. The LP problem is optimal.

else

choose the leaving variable xB[r] = xk 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, 15th line from top, the sentence reads:

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

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

Chapter 8:

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

There are elements in vector h1 that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that hil ≤ 0, therefore $$\frac{x_{B[i]}} {h_{il}}$$ is not defined):

There are elements in vector h1 that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that hil ≤ 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:

s0 = jPλjsj

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 dB ≥ 0 then

if s0 = 0 then STOP. (LP.1) is optimal.

It should be as follows:

s0 = jPλjsj

and the direction

dB = −jPλjhj, where hj = AB−1A. j.

Step 2.1. (Test of Optimality).

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

else

if dB ≥ 0 then

if s0 = 0 then STOP. (LP.1) is optimal.