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An implementation of the direct algorithm

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(13)

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(19)

1e-08

1e-07

1e-06

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0.0001

0.001

0.01

0.1

1

10

100

1000

0

100

200

300

400

500

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Minimal function value

Number of function-evaluations

The first test-function

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1e-08

1e-07

1e-06

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0.001

0.01

0.1

1

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100

1000

0

50

100

150

200

250

300

350

400

Function value

Number of function evaluations

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(20)

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5

-4

-3

-2

-1

0

1

2

3

4

5

The first test-function

’alt_00.dat’

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1e-20

1e-10

1

1e+10

0

100

200

300

400

500

600

700

Minimal function value

Number of function-evaluations

The second test-function

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0

200

400

600

800

1000

1200

1400

1600

0

5

10

15

20

25

Function value

Number of function evaluations

Linesearch

Trust region

\ 7F9e©`:M;>=sZ`_BABCEJGtEJIeGL`;S:M;uap©cbGM7FE3TvEJIeGL;wIS©`Tcdf

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(21)

−5

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5

−5

0

5

0

10

20

30

40

50

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(22)

1e-20

1e-10

1

0

100

200

300

400

500

600

700

Minimal function value

º

Number of function-evaluations

The third test-function

\ 79e©:M; =^»`_BADCFEJGVEJI4GL;:M;bad©cdG7FEJTEHIeGML;SIS©Tcgf G7E3TihHOJC½©;SjUkilnm^o"p`q3r

0.1

1

10

100

0

10

20

30

40

50

60

70

80

Function value

Number of function evaluations

Linesearch

Trust region

\ 7F9e©`:M;>=@ $_BABCEJGtEJIeGL`;S:M;uap©cbGM7FE3TvEJIeGL;wIS©`Tcdf G7FEJTxhHOJC½©;yjUkzN<GM;u;bQ;bN<G<f{a;uN<cu;bT"G|OJTa}aEJ9Hf~C;u9 G:&©`N<G:M;b937FE3T

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 2 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 3 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 4 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 5 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 6 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 7 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 8 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

Points which where sampled after 9 Iterations

-5

-4

-3

-2

-1

0

1

2

3

4

-5

-4

-3

-2

-1

0

1

2

3

4

The third test-function

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(23)

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