| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
|---|
| 1 |
|
Function |
Beale function |
Booth function |
Camel3 function |
Cube function |
Freudstein Roth function |
McCormick function |
| 2 | Quasi-Newton method |
Starting point |
(3, 0) |
(2, -1) |
(0, 1) |
(-2, 1) |
(2, 1) |
(-1, 5) |
(-5, 5) |
(-5, -2) |
(2, 2) |
(-3, -3) |
(4, -4) |
(-5, 5) |
(0, 0) |
(3, 3) |
(4, 5) |
(5, -5) |
(5, 7) |
(3, 2) |
(1, 0) |
(-1, -2) |
(-1, -1) |
(0, 0) |
(0, 2) |
(3, 3) |
| 3 | BFGS – Solve3 – Default step 4 |
Number of iterations |
7 |
9 |
0 |
15 |
4 |
2 |
4 |
4 |
6 |
7 |
6 |
6 |
22 |
25 |
28 |
124 |
4 |
2 |
5 |
3 |
4 |
14 |
7 |
13 |
| 4 | Result |
(3.00000, 0.499999) |
(3.00000, 0.500000) |
(0, 1) |
(2.99999, 0.499998) |
(1,3) |
(1,3) |
(1,3) |
(1,3) |
(1.74755, -0.873778) |
(-1.74755, 0.873776) |
(-1.40873e-05, 8.36144e-06) |
(3.15455e-05, -2.08159e-05) |
(1,1) |
(1.00000, 0.999999) |
(1.00000, 1.00000) |
(1.00000, 1.00001) |
(-15.5583, 4.56866) |
(3.93979, 2.34174) |
(3.43127, -1.29338) |
(15.1835, -0.145270) |
(-0.547197, -1.54720) |
(-865968, -865969) |
(-60.2375, -61.2375) |
(-44.5295, -45.5295) |
| 5 | Distance to minimum |
1.00E-06 |
0 |
3.04138 |
0.000010198 |
0 |
0 |
0 |
0 |
1.95382 |
1.95382 |
0.0000163819 |
0.0000377944 |
0 |
1.00E-06 |
0 |
0.00001 |
20.5662 |
1.96822 |
5.52094 |
10.9949 |
0.0000122066 |
1.22E+06 |
84.4148 |
62.2004 |
| 6 | Function value |
1.02E-12 |
2.01E-15 |
14.203125 |
1.56E-11 |
9.74E-18 |
0 |
3.50E-14 |
4.01E-20 |
0.298638442243012 |
0.298638442236861 |
3.49E-10 |
1.77E-09 |
7.90E-19 |
1.04E-12 |
7.21E-13 |
1.75E-11 |
882.752952450238 |
1562.46913854855 |
75.8100260354757 |
145.078183901214 |
-1.91322295498084 |
-865969.361814367 |
-61.6034833731871 |
-45.8955201052377 |
| 7 | LBFGS – Default step 4 |
Number of iterations |
8 |
9 |
0 |
10 |
5 |
2 |
4 |
4 |
8 |
8 |
9 |
12 |
23 |
27 |
34 |
37 |
3 |
4 |
5 |
12 |
5 |
5 |
6 |
5 |
| 8 | Result |
(3.00, 0.50) |
(3.00, 0.50) |
(0, 1) |
(3.00, 0.50) |
(1,3) |
(1,3) |
(1,3) |
(1,3) |
(-7.21593e-07, 1.79620e-07) |
(-7.06236e-11, 3.14468e-10) |
(1.74755, -0.873780) |
(3.24446e-11, -7.11146e-11) |
(1,1) |
(1,1) |
(1,1) |
(1,1) |
(4.42786, 3.95197) |
(23.2839, -0.0285399) |
(3.76665, -1.32463) |
(10.6354, -0.962592) |
(-0.547198, -1.54720) |
(-0.547197, -1.54720) |
(-13.1136, -14.1136) |
(2.59440, 1.59440) |
| 9 | Distance to minimum |
0 |
0 |
3.04138 |
0 |
0 |
0 |
0 |
0 |
7.44E-07 |
3.22E-10 |
1.95382 |
7.82E-11 |
0 |
0 |
0 |
0 |
0.574152 |
18.7224 |
5.4656 |
7.509 |
0.0000128062 |
0.0000122066 |
17.7716 |
4.44288 |
| 10 | Function value |
1.56E-14 |
8.13E-14 |
14.203125 |
8.43E-14 |
0 |
1.03E-29 |
0 |
0 |
9.44E-13 |
8.67E-20 |
0.298638442250412 |
4.86E-21 |
9.42E-14 |
9.49E-16 |
2.75E-14 |
3.17E-17 |
6.56262722589618 |
135.278205039916 |
73.0512445293543 |
49.4194259805292 |
-1.91322295498104 |
-1.91322295498088 |
-14.4795935671925 |
1.22836969860876 |
| 11 | DmLBFGS – Default step 4 and momentum 0.01 |
Number of iterations |
10 |
12 |
0 |
694 |
7 |
2 |
9 |
9 |
9 |
12 |
4 |
12 |
23 |
2 |
2 |
59 |
1 |
2 |
1 |
1 |
5 |
7 |
10 |
6 |
| 12 | Result |
(3.00, 0.50) |
(3.00000, 0.500001) |
(0, 1) |
(-137209, 1.00001) |
(0.999999, 3.00000) |
(0.983160, 3.01684) |
(1,3) |
(0.999998, 3.00000) |
(7.47134e-07, -1.68573e-06) |
(-1.00095e-06, 1.41276e-06) |
(-0.0167967, -0.0286764) |
(2.69254e-07, -6.04864e-07) |
(1, 1) |
(0.149412, 3.10558) |
(0.142150, 5.08037) |
(0.999999, 0.999997) |
(4.92953, 6.01251) |
(16.0046, 2.92309) |
(2.83208, -1.09925) |
(-1.05114, -1.01132) |
(-0.547188, -1.54720) |
(-0.547199, -1.54720) |
(-0.547193, -1.54720) |
(2.59439, 1.59440) |
| 13 | Distance to minimum |
0 |
1.00E-06 |
3.04138 |
137212 |
1.00E-06 |
0.0238154 |
0 |
2.00E-06 |
1.84E-06 |
1.73E-06 |
0.0332335 |
6.62E-07 |
0 |
2.2709 |
4.16957 |
3.16E-06 |
2.01374 |
11.0572 |
5.54096 |
7.85682 |
0.000010198 |
0.0000134536 |
0.0000104403 |
4.44287 |
| 14 | Function value |
9.75E-15 |
1.96E-12 |
14.203125 |
0.452020049962163 |
5.49E-12 |
3.01E-05 |
8.86E-13 |
1.78E-11 |
2.40E-12 |
2.43E-12 |
5.42E-04 |
2.97E-13 |
6.13E-15 |
964.268205697261 |
2580.94643669169 |
8.85E-13 |
23951.2334624963 |
632.997861929357 |
115.514941015128 |
293.479274072668 |
-1.91322295495376 |
-1.91322295497782 |
-1.91322295495796 |
1.22836969861451 |
| 15 | DmLBFGS – Default step 4 and momentum 0.1 |
Number of iterations |
1 |
1 |
0 |
5 |
1 |
2 |
14 |
2 |
14 |
15 |
2 |
2 |
28 |
2 |
2 |
3 |
1 |
1 |
1 |
1 |
1 |
12 |
8 |
4 |
| 16 | Result |
(2.80429, 0.335507) |
(1.70396, -0.150082) |
(0, 1) |
(-0.809168, 1.70512) |
(2.40249, 1.80498) |
(0.827608, 3.17239) |
(0.999994, 3.00001) |
(0.0273837, 2.90196) |
(2.18751e-06, -3.62317e-07) |
(1.74755, -0.873776) |
(-1.67223, -3.97001) |
(0.219181, 4.98997) |
(1.00000, 0.999999) |
(0.791619, 3.08179) |
(-0.461242, 5.09294) |
(-1.49342, -4.91342) |
(4.93594, 6.10228) |
(3.84581, 2.30757) |
(2.66553, -0.999318) |
(-1.04649, -1.10120) |
(-0.390821, -1.66250) |
(-0.547201, -1.54720) |
(-0.532360, -1.67301) |
(2.60080, 1.59547) |
| 17 | Distance to minimum |
0.255657 |
1.45E+00 |
3.04138 |
3.99526 |
1.84E+00 |
0.243798 |
0.0000116619 |
9.78E-01 |
2.22E-06 |
1.95E+00 |
4.30782 |
4.99E+00 |
1.00E-06 |
2.09219 |
4.34596 |
6.41761 |
2.10326 |
2.04853 |
5.51751 |
7.9109 |
0.194288 |
0.0000148661 |
0.126691 |
4.44816 |
| 18 | Function value |
8.16E-02 |
1.32E+00 |
14.203125 |
1.61754686750773 |
3.78E+00 |
3.21E-03 |
6.40E-11 |
4.25E-01 |
8.56E-12 |
2.99E-01 |
2.85E+01 |
2.91E+01 |
3.56E-14 |
793.882969610977 |
3287.32929203811 |
7.29E+00 |
23951.2334624963 |
1562.46913854855 |
115.514941015128 |
293.479274072668 |
-1.74213821714839 |
-1.91322295495903 |
-1.91029820295244 |
1.22837301519369 |
| 19 | DmLBFGS – Default step 4 and momentum 0.9 |
Number of iterations |
1 |
1 |
0 |
2 |
1 |
2 |
2 |
2 |
2 |
3 |
2 |
2 |
1 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
| 20 | Result |
(2.97825, 0.0372786) |
(1.96711, -0.905565) |
(0, 1) |
(-1.79358, -0.644633) |
(2.04472, 1.08944) |
(-0.784331, 4.78433) |
(-4.74242, 5.16388) |
(-4.44185, -1.45302) |
(1.69775, 1.78393) |
(-2.30148, -2.95646) |
(3.55530, -3.99768) |
(-4.41733, 4.99889) |
(0.0255778, 0.00000) |
(2.66779, 3.01230) |
(3.54809, 5.00941) |
(4.15325, -4.98871) |
(4.99288, 6.90025) |
(3.09398, 2.03417) |
(1.18506, -0.111035) |
(-1.00517, -1.90013) |
(-0.932313, -1.07361) |
(0.0141421, -0.0989949) |
(0.154860, 1.84074) |
(3.01541, 2.90120) |
| 21 | Distance to minimum |
0.463232 |
1.74427 |
3.04138 |
4.92835 |
2.17754 |
2.52342 |
6.13659 |
7.03158 |
2.46267 |
3.74666 |
5.34992 |
6.67096 |
1.39624 |
2.61359 |
4.75059 |
6.76813 |
2.90026 |
2.73814 |
5.60842 |
8.41865 |
0.610408 |
1.55318 |
3.45991 |
5.69915 |
| 22 | Function value |
0.0816002048334095 |
1.32034383860438 |
14.203125 |
4.1510780781747 |
3.78359213500126 |
0.460239406396516 |
31.6863439543563 |
7.11958856270286 |
0.187239436105983 |
6.3048575110819 |
14.4164010185532 |
24.5506505634639 |
0.581867472626275 |
839.635549231954 |
2520.66688797003 |
14479.1433447801 |
23951.2334624963 |
1562.46913854855 |
115.514941015128 |
293.479274072668 |
-1.74213821714839 |
-1.15731395572753 |
3.18703095912642 |
1.70444281974627 |
| 23 | DmLBFGS – Default step 4 and momentum 0.99 |
Number of iterations |
1 |
1 |
0 |
2 |
1 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
| 24 | Result |
(2.99783, 0.00372786) |
(1.99671, -0.990556) |
(0, 1) |
(-1.97719, -0.960731) |
(2.00447, 1.00894) |
(-0.978398, 4.97840) |
(-4.97424, 5.01639) |
(-4.94418, -1.94530) |
(1.96785, 1.97703) |
(-2.96270, -2.99768) |
(3.95333, -3.99976) |
(-4.94206, 4.99989) |
(0.00255778, 0.00000) |
(2.96536, 3.00128) |
(3.95558, 5.00093) |
(4.90849, -4.99878) |
(4.99929, 6.99003) |
(3.00940, 2.00342) |
(1.01851, -0.0111035) |
(-1.00052, -1.99001) |
(-0.993231, -1.00736) |
(0.00141421, -0.00989949) |
(0.0154925, 1.98407) |
(3.00154, 2.99012) |
| 25 | Distance to minimum |
0.496277 |
1.79676 |
3.04138 |
5.18711 |
2.23E+00 |
2.79788 |
6.30534 |
7.73E+00 |
2.79E+00 |
4.21E+00 |
5.62378 |
7.03E+00 |
1.41241 |
2.80495 |
4.97422 |
7.15972 |
2.99003 |
2.81937 |
5.65166 |
8.47859 |
0.700264 |
1.63225 |
3.57581 |
5.76027 |
| 26 | Function value |
8.16E-02 |
1.32E+00 |
14.203125 |
4.82266977376039 |
3.78E+00 |
5.83E-01 |
3.31E+01 |
8.59E+00 |
2.70E-01 |
8.86E+00 |
1.48E+01 |
2.40E+01 |
5.82E-01 |
868.274668601301 |
2408.27976294674 |
7.13E+04 |
23951.2334624963 |
1562.46913854855 |
115.514941015128 |
293.479274072668 |
-1.74213821714839 |
-1.15731395572753 |
3.48833375360427 |
1.70444281974627 |
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