ERRATA Applied Optimization with MATLAB Programming, Second Edition        P.Venkataraman       John Wiley (2009)
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Applied Optimization with MATLAB Programming, Second Edition
P.Venkataraman
John Wiley (2009)

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 x1 x2 x3 x4 x5 b 0 0.7333 1 -0.1333 0 5.1667 1 -0.3333 0 0.3333 0 8.3333 0 7 0 -1 1 45 0 -1230 0 330 0 13500

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x1  =  800;       x2  =  1200,     f = 16800  or \$ 168.00                                    (3.27)

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Table 3.7   Example 3.2: Simplex Table 2, Phase I (canonical form)
 x1 x2 s1 s2 a1 s3 s4 b 0 0 1 1 -1 0 0 1,360 1 1 0 -1 1 0 0 640 0 -1 0 1 -1 1 0 160 0 1 0 0 0 0 1 1,440 0 0.4 0 -1.4 1.4 0 0 f-18,224 0 0 0 0 1 0 0 Af

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The unit vector [1 0 0 0 0 ]T must be constructed under the x2 column

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Simplex Table 2:  Using the pivot row identified in the last table, the unit vector [0 0 1 0]T under the s2 column

are to transfer the unit vector [1 0 0 0]T from the s1 column to the x2 column.

Simplex Table 3: Table 3.19 denotes the reduced table with the canonical form after the required row operations are completed. The basis variables are x2, x4, s3. The first row is the pivot row. The EBV is x1 and the LBV is x2. The pivot row is the first row.

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x =  9.091,      x4  =  61.364,     x =  0,       x3  =  0,      s1 = 0,    s2 = 0,     s3 = 359.091,    f  =  -1281.82

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After the introduction of the slack variables (s1, s2, s3, s4) the solution to the primal problem

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page 191

Since x1 and x3 are basic,  with the reduced coat coefficient of 0, the corresponding slack/surplus s1, s3 variables will be zero, as observed in Table 3.31.

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x1* = 10.4761,    x2* = 6.4285,   x3* = 0.4524,   f* = -21407.14

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From this discussion it is apparent that to keep the location the original solution unchanged, c1 must be less than   -450.

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page 202

Problem 3.14

Problem 3.15

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page 239

Equation (4.70a) is incorrect.  It is based on Equation (4.48b) which is correct.  This error is propogated is severla pages where this constraint is handled.

(4.70b)

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(4.71b)

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(4.80)

(4.81)

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(4.82a)

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(4.90b)

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( The first equation in the Lagrange Multiplier Method Sub-section)

(4.91)

(4.92a)

(4.92d)

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page 259

4.6.      Proove that the function will not change along the tangent

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4.8       Express the Taylor series expansion (quadratic) of the function f(x) = (2 –3x  + x2) sin x about the point x = 0.707. Confirm your results through the Symbolic Math Toolbox.  Plot the original function and the approximation.

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page 333

6.3  Apply the Pattern Search method to Example 5.3

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6.6       Translate the Powell method into working MATLAB code. Verify solution to Example 6.1 and Example 5.3. Start from several points and verify that number of cycles to converge is the same.

6.19     Start the Steepest Descent method from different points for problem below and identify where the solution requires more than 15 iterations.

6.24     Example 6.2 was explicitly created to challenge the numerical techniques for unconstrained optimization.  There are many other similar test problems.  A problem with steep minimum (Beale, Survey of Integer Programming) is

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