--------------------------- HW05 CALCULATIONS ------------------------- ------------------- Trust-Region Quasi-Newton (SR1/Exact) ------------------- EDU> x0 = [0.2;-1.0]; sr1t SR1/Trust Region minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 2.0000e-001 -1.0000e+000 6.6116e+000 1.00e-001 1 2.9952e-001 -1.0098e+000 5.9821e+000 1.00e-001 1.0000 0.991 5.0e+000 2.9e-001 2 4.9620e-001 -1.0461e+000 4.9731e+000 2.00e-001 1.0000 0.981 2.6e+000 4.1e-001 3 8.9411e-001 -1.0874e+000 4.1477e+000 4.00e-001 1.0001 0.869 9.4e-001 8.3e-001 4 9.4241e-001 -1.0104e+000 3.9061e+000 8.00e-001 0.1136 1.928 7.1e-002 6.8e-001 5 1.5355e+000 -4.6947e-001 2.2734e+000 8.00e-001 1.0034 0.841 2.8e+000 5.0e-001 6 2.7385e+000 5.8601e-001 1.2649e+000 1.60e+000 1.0002 0.522 3.9e+000 1.7e+000 7 2.7385e+000 5.8601e-001 1.2649e+000 1.60e+000 0.4836 -0.019 9.3e-001 1.7e+000 8 2.6573e+000 4.0952e-001 1.0144e+000 1.93e-001 1.0044 0.632 6.5e-001 3.4e-001 9 2.6686e+000 4.0963e-001 1.0131e+000 1.93e-001 0.0584 1.842 4.2e-003 2.9e-001 10 2.7750e+000 4.2955e-001 1.0060e+000 1.93e-001 0.5601 1.322 4.9e-002 6.6e-002 11 2.9137e+000 4.8148e-001 1.0008e+000 1.93e-001 0.7653 1.166 1.2e-001 1.0e-001 12 2.9137e+000 4.8148e-001 1.0008e+000 1.93e-001 0.6631 -0.002 4.3e-002 1.0e-001 13 2.9454e+000 4.8613e-001 1.0003e+000 3.21e-002 1.0000 0.946 4.5e-002 2.8e-002 14 2.9863e+000 4.9638e-001 1.0000e+000 6.41e-002 0.6574 1.215 2.1e-002 3.2e-003 15 2.9990e+000 4.9981e-001 1.0000e+000 6.41e-002 0.2045 1.054 6.9e-003 1.7e-003 16 3.0000e+000 4.9999e-001 1.0000e+000 6.41e-002 0.0163 0.984 3.7e-004 6.8e-005 17 3.0000e+000 5.0000e-001 1.0000e+000 6.41e-002 0.0003 1.058 1.7e-005 2.8e-006 18 3.0000e+000 5.0000e-001 1.0000e+000 6.41e-002 0.0000 1.000 1.6e-006 3.2e-009 Hessian update skipped. 19 3.0000e+000 5.0000e-001 1.0000e+000 6.41e-002 0.0000 0.000 1.2e-009 3.2e-009 Best point: x' = 2.9999999970711420e+000 4.9999999937669160e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 19 Trust-Region passes. Stopped by: e1 < eta1. Flop count: 6529 total--average 344 per step. EDU> x0 = [1.0;0.8]; sr1t SR1/Trust Region minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 1.0000e+000 8.0000e-001 5.9144e+000 1.00e-001 1 1.0229e+000 7.0266e-001 5.1300e+000 1.00e-001 1.0000 0.938 1.8e+000 9.1e-001 2 1.1314e+000 5.3451e-001 3.9016e+000 2.00e-001 1.0005 1.026 8.8e-001 8.4e-001 3 1.4295e+000 2.6778e-001 2.2766e+000 4.00e-001 1.0000 0.994 1.2e+000 1.5e+000 4 1.9713e+000 -6.1493e-002 1.4298e+000 8.00e-001 0.7926 0.909 1.2e+000 4.3e-001 5 1.9403e+000 -3.7932e-003 1.3826e+000 8.00e-001 0.0819 1.550 9.4e-001 7.7e-001 6 2.5775e+000 4.8255e-001 1.1078e+000 8.00e-001 1.0021 0.301 2.8e+002 1.4e+000 7 2.5775e+000 4.8255e-001 1.1078e+000 8.00e-001 0.2473 0.186 3.6e-001 1.4e+000 8 2.5946e+000 4.3611e-001 1.0419e+000 4.95e-002 1.0002 0.933 2.0e-001 9.1e-001 9 2.6913e+000 4.1458e-001 1.0109e+000 9.89e-002 1.0015 1.068 5.1e-002 2.4e-001 10 2.7689e+000 4.3051e-001 1.0059e+000 1.98e-001 0.4004 1.499 3.8e-002 6.2e-002 11 2.9264e+000 4.8728e-001 1.0009e+000 1.98e-001 0.8457 1.050 1.3e-001 1.4e-001 12 2.9264e+000 4.8728e-001 1.0009e+000 1.98e-001 1.0000 -0.032 2.0e-004 1.4e-001 13 2.9197e+000 4.7557e-001 1.0007e+000 4.95e-002 0.2725 0.245 2.4e-002 3.7e-002 14 2.9210e+000 4.7867e-001 1.0006e+000 3.37e-003 1.0008 1.016 1.9e-002 2.5e-002 15 2.9272e+000 4.8133e-001 1.0005e+000 6.74e-003 1.0000 1.109 1.3e-002 3.8e-002 16 2.9403e+000 4.8468e-001 1.0003e+000 1.35e-002 1.0000 0.994 3.8e-002 2.9e-002 17 2.9663e+000 4.9159e-001 1.0001e+000 2.70e-002 1.0000 1.014 2.9e-002 1.8e-002 18 2.9969e+000 4.9938e-001 1.0000e+000 5.39e-002 0.5849 1.070 1.6e-002 4.1e-003 19 2.9998e+000 4.9992e-001 1.0000e+000 5.39e-002 0.0544 0.996 1.1e-003 3.6e-004 20 2.9998e+000 4.9993e-001 1.0000e+000 5.39e-002 0.0006 1.843 2.4e-005 2.9e-004 21 3.0000e+000 5.0000e-001 1.0000e+000 5.39e-002 0.0039 1.000 1.4e-004 4.7e-007 22 3.0000e+000 5.0000e-001 1.0000e+000 5.39e-002 0.0000 0.999 3.5e-008 2.5e-009 Best point: x' = 2.9999999982302300e+000 4.9999999966010540e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 22 Trust-Region passes. Stopped by: e1 < eta1. Flop count: 8526 total--average 388 per step. EDU> x0 = [0.1;-2.6]; sr1t SR1/Trust Region minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 1.0000e-001 -2.6000e+000 5.9374e+000 1.00e-001 1 1.0000e-001 -2.6000e+000 5.9374e+000 1.00e-001 1.0000 -10.067 3.5e+000 8.8e-002 2 1.0983e-001 -2.5770e+000 5.9320e+000 2.50e-002 1.0000 0.606 1.2e-001 4.9e-002 3 1.0805e-001 -2.5787e+000 5.9314e+000 2.50e-002 0.0994 1.139 1.6e-002 1.8e-002 4 1.0853e-001 -2.5725e+000 5.9312e+000 2.50e-002 0.2499 1.993 4.5e-003 1.5e-002 5 1.1128e-001 -2.5477e+000 5.9303e+000 2.50e-002 1.0000 0.998 7.0e-002 1.7e-002 6 1.1707e-001 -2.4980e+000 5.9276e+000 5.00e-002 1.0000 1.006 9.3e-002 2.1e-002 7 1.1707e-001 -2.4980e+000 5.9276e+000 1.00e-001 1.0000 -1.815 1.3e-001 2.1e-002 8 1.2311e-001 -2.4737e+000 5.9266e+000 2.50e-002 1.0001 0.355 6.5e-002 7.5e-002 9 1.2598e-001 -2.4489e+000 5.9240e+000 2.50e-002 1.0017 1.619 7.4e-002 7.1e-002 10 1.3118e-001 -2.3991e+000 5.9179e+000 5.00e-002 1.0005 0.984 1.7e-001 5.1e-002 11 1.4483e-001 -2.3000e+000 5.9023e+000 1.00e-001 1.0000 0.999 2.2e-001 4.5e-002 12 1.7330e-001 -2.1021e+000 5.8574e+000 2.00e-001 1.0000 0.922 3.0e-001 5.7e-002 13 2.3327e-001 -1.7066e+000 5.7711e+000 4.00e-001 1.0000 0.670 6.5e-001 1.8e-001 14 2.9734e-001 -1.3118e+000 5.7386e+000 4.00e-001 1.0000 0.904 3.0e-001 2.8e-001 15 2.9734e-001 -1.3118e+000 5.7386e+000 8.00e-001 1.0000 -0.004 5.2e-002 2.8e-001 16 4.6876e-001 -1.2087e+000 5.0311e+000 2.00e-001 1.0001 0.681 1.6e-001 3.3e-001 17 6.4367e-001 -1.1116e+000 4.4959e+000 2.00e-001 1.0000 1.145 9.0e-001 3.3e-001 18 9.6755e-001 -8.7610e-001 3.6070e+000 4.00e-001 1.0011 1.177 1.4e+000 4.2e-001 19 1.5814e+000 -3.6298e-001 2.0678e+000 8.00e-001 1.0000 0.937 6.5e+000 6.7e-001 20 1.5814e+000 -3.6298e-001 2.0678e+000 1.60e+000 1.0000 0.180 4.2e+000 6.7e-001 21 1.8991e+000 -1.1966e-001 1.5287e+000 4.00e-001 1.0005 1.453 8.1e-001 4.9e-001 22 2.5194e+000 3.8593e-001 1.0381e+000 8.00e-001 1.0002 0.937 5.0e+000 7.2e-001 23 2.5324e+000 3.8379e-001 1.0337e+000 1.60e+000 0.0082 1.865 5.6e-003 6.4e-001 24 2.5324e+000 3.8379e-001 1.0337e+000 1.60e+000 0.5970 -5.082 8.6e-001 6.4e-001 25 2.7684e+000 4.2042e-001 1.0078e+000 2.39e-001 1.0005 0.982 9.9e-002 1.1e-001 26 2.7684e+000 4.2042e-001 1.0078e+000 4.78e-001 1.0020 -5.712 3.7e+000 1.1e-001 27 2.7962e+000 4.3383e-001 1.0053e+000 1.20e-001 0.2575 1.805 3.2e-002 8.2e-002 28 2.9068e+000 4.8037e-001 1.0010e+000 1.20e-001 1.0032 0.882 1.6e-001 1.2e-001 29 2.9515e+000 4.9001e-001 1.0003e+000 2.39e-001 0.1911 1.461 2.0e-002 6.2e-002 30 2.9892e+000 4.9724e-001 1.0000e+000 2.39e-001 0.1604 1.121 1.5e-002 4.0e-003 31 3.0007e+000 5.0047e-001 1.0000e+000 2.39e-001 0.0501 0.814 6.5e-003 4.6e-003 32 2.9997e+000 4.9998e-001 1.0000e+000 2.39e-001 0.0046 1.125 9.8e-004 9.2e-004 33 3.0000e+000 5.0000e-001 1.0000e+000 2.39e-001 0.0011 1.001 8.5e-005 1.1e-006 34 3.0000e+000 5.0000e-001 1.0000e+000 2.39e-001 0.0000 1.003 3.0e-007 1.5e-009 Best point: x' = 2.9999999959003050e+000 4.9999999885277810e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 34 Trust-Region passes. Stopped by: e1 < eta1. Flop count: 13347 total--average 393 per step. ----------------------------- Pure Newton ----------------------------- EDU> fname = 'uvw'; dfname = 'uvwd'; hfname = 'uvwh'; EDU> x0 = [0.2;-1.0]; newton Pure Newton minimization of function "uvw", using gradient "uvwd" and Hessian "uvwh": k x_k(1) x_k(2) f(x_k) dx(rel) grad(rel) pred obj dec 0 2.0000e-001 -1.0000e+000 6.6116e+000 2.0e+000 1.9e+000 1.7e+001 1 7.5659e-001 3.1181e-001 4.4958e+000 2.0e+000 6.4e-001 3.2e+000 2 3.0248e+000 -5.2903e-001 6.2448e+000! 2.0e+000 4.7e+000 5.8e+002 3 1.5593e+000 -5.7471e-001 2.4795e+000 6.4e-001 1.3e+000 4.8e+000 4 2.7136e+000 4.5166e-001 1.0171e+000 2.0e+000 7.1e-001 1.7e+000 5 2.8887e+000 4.6914e-001 1.0012e+000 6.2e-002 1.1e-001 1.2e-002 6 2.9859e+000 4.9776e-001 1.0000e+000 5.9e-002 9.1e-002 1.1e-002 7 2.9993e+000 4.9984e-001 1.0000e+000 4.5e-003 3.1e-004 1.3e-009 8 3.0000e+000 5.0000e-001 1.0000e+000 3.3e-004 3.3e-006 1.4e-011 9 3.0000e+000 5.0000e-001 1.0000e+000 2.6e-007 1.3e-012 1.5e-024 Best point: x[9]' = 2.9999999999984820e+000 4.9999999999963600e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 9 pure Newton steps. Stopped by: test 1, test 2, test 3. Flop count: 2321 total--average 258 per step. EDU> x0 = [1.0;0.8]; newton Pure Newton minimization of function "uvw", using gradient "uvwd" and Hessian "uvwh": k x_k(1) x_k(2) f(x_k) dx(rel) grad(rel) pred obj dec 0 1.0000e+000 8.0000e-001 5.9144e+000 1.3e+000 3.2e+000 7.3e+001 1 -1.7140e+000 1.2602e+000 2.7395e+000 2.0e+000 5.8e+000 1.8e+003 2 -2.7596e+000 1.4238e+000 4.5551e+000! 4.7e-001 3.4e+001 1.3e+005 3 -2.3860e+000 1.3627e+000 1.7498e+000 1.5e-001 1.0e+001 4.6e+003 4 -2.1133e+000 1.3534e+000 1.5302e+000 1.2e-001 2.3e+000 1.1e+002 5 3.3192e-001 1.6653e+000 1.3828e+001! 2.0e+000 6.2e+000 2.8e+003 6 2.1257e-001 1.3385e+000 9.4292e+000 4.4e-001 1.1e+000 8.7e+001 7 8.8634e-002 1.0990e+000 8.2329e+000 8.2e-001 2.9e-001 4.2e+000 8 1.2575e-002 1.0082e+000 8.1030e+000 1.5e+000 2.7e-002 3.5e-002 9 1.5066e-004 1.0000e+000 8.1016e+000 2.0e+000 2.7e-004 2.5e-006 10 1.0979e-008 1.0000e+000 8.1016e+000 2.0e+000 1.9e-008 6.6e-015 Best point: x[10]' = 1.0978581259531420e-008 1.0000000018193520e+000. Best value: uvw(x) = 8.1015625000000000e+000. Step count: 10 pure Newton steps. Stopped by: test 3. Flop count: 2534 total--average 253 per step. EDU> x0 = [0.1;-2.6]; newton Pure Newton minimization of function "uvw", using gradient "uvwd" and Hessian "uvwh": k x_k(1) x_k(2) f(x_k) dx(rel) grad(rel) pred obj dec 0 1.0000e-001 -2.6000e+000 5.9374e+000 2.0e+000 1.2e+000 9.7e+001 1 1.0010e-001 -2.6524e+000 5.9323e+000 2.0e-002 7.2e-002 9.9e-001 2 1.0051e-001 -2.6448e+000 5.9323e+000 4.2e-003 3.1e-004 1.8e-005 3 1.0054e-001 -2.6445e+000 5.9323e+000! 2.3e-004 6.4e-007 7.5e-011 4 1.0054e-001 -2.6445e+000 5.9323e+000 3.0e-008 4.5e-015 3.2e-027 Best point: x[4]' = 1.0053793732415940e-001 -2.6445135850231140e+000. Best value: uvw(x) = 5.9322561423777800e+000. Step count: 4 pure Newton steps. Stopped by: test 1, test 2, test 3. Flop count: 1154 total--average 289 per step. -------------------- Trust-Region Newton (Exact Hessian; Dogleg) -------------------- EDU> x0 = [0.2;-1.0]; dogleg Newton/Trust Region minimization of function "uvw", using gradient "uvwd", Hessian "uvwh": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 2.0000e-001 -1.0000e+000 6.6116e+000 1.00e-001 1 2.9952e-001 -1.0098e+000 5.9821e+000 1.00e-001 1.0000 0.999 2.8e+000 2.9e-001 2 4.9789e-001 -1.0353e+000 4.9705e+000 2.00e-001 1.0000 0.991 2.4e+000 4.2e-001 3 8.9598e-001 -1.0743e+000 4.1069e+000 4.00e-001 1.0000 0.930 4.9e+000 7.9e-001 4 9.1766e-001 -8.3531e-001 3.6500e+000 8.00e-001 0.3000 1.263 2.8e+000 5.3e-001 5 1.6485e+000 -5.0999e-001 2.3071e+000 8.00e-001 1.0000 1.079 7.9e+000 5.3e-001 6 2.6636e+000 4.6465e-001 1.0419e+000 1.60e+000 0.8795 1.030 1.9e+000 9.5e-001 7 2.8799e+000 4.6422e-001 1.0015e+000 1.60e+000 0.1352 0.999 8.1e-002 4.0e-002 8 2.9894e+000 4.9936e-001 1.0001e+000 1.60e+000 0.0719 0.974 7.6e-002 3.9e-002 9 2.9996e+000 4.9990e-001 1.0000e+000 1.60e+000 0.0064 1.002 3.4e-003 8.4e-005 10 3.0000e+000 5.0000e-001 1.0000e+000 1.60e+000 0.0003 1.000 2.1e-004 4.1e-007 11 3.0000e+000 5.0000e-001 1.0000e+000 1.60e+000 0.0000 0.998 5.4e-008 4.0e-014 Best point: x' = 2.9999999999999000e+000 4.9999999999997480e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 11 Trust-Region passes. Stopped by: e1 < eta1 and e2 < eta2. Flop count: 3486 total--average 317 per step. EDU> x0 = [1.0;0.8]; dogleg Newton/Trust Region minimization of function "uvw", using gradient "uvwd", Hessian "uvwh": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 1.0000e+000 8.0000e-001 5.9144e+000 1.00e-001 1 1.0229e+000 7.0266e-001 5.1300e+000 1.00e-001 1.0000 1.006 2.7e+000 9.1e-001 2 1.0933e+000 5.1545e-001 3.9315e+000 2.00e-001 1.0000 1.016 1.0e+001 8.3e-001 3 1.3265e+000 1.9050e-001 2.4178e+000 4.00e-001 1.0000 1.012 2.5e+000 1.4e+000 4 2.0908e+000 -4.6063e-002 1.3920e+000 8.00e-001 1.0000 0.860 7.4e-001 4.8e-002 5 2.6074e+000 5.5159e-001 1.2533e+000 1.60e+000 0.4937 0.322 1.3e+001 1.7e+000 6 3.0594e+000 4.9864e-001 1.0033e+000 1.60e+000 0.2844 0.918 1.7e-001 3.1e-001 7 2.9708e+000 4.9217e-001 1.0001e+000 1.60e+000 0.0555 0.974 2.9e-002 6.3e-003 8 2.9990e+000 4.9986e-001 1.0000e+000 1.60e+000 0.0183 1.014 1.6e-002 2.2e-003 9 3.0000e+000 5.0000e-001 1.0000e+000 1.60e+000 0.0006 1.001 3.3e-004 1.5e-006 10 3.0000e+000 5.0000e-001 1.0000e+000 1.60e+000 0.0000 1.000 1.8e-006 3.2e-011 11 3.0000e+000 5.0000e-001 1.0000e+000 1.60e+000 0.0000 0.000 6.9e-012 3.2e-011 Best point: x' = 2.9999999999807800e+000 4.9999999999656000e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 11 Trust-Region passes. Stopped by: e1 < eta1. Flop count: 3477 total--average 316 per step. EDU> x0 = [0.1;-2.6]; dogleg Newton/Trust Region minimization of function "uvw", using gradient "uvwd", Hessian "uvwh": k x_k(1) x_k(2) f(x_k) Delta |dx|/Delta RR e_1 e_2 0 1.0000e-001 -2.6000e+000 5.9374e+000 1.00e-001 1 1.0010e-001 -2.6524e+000 5.9323e+000 1.00e-001 0.5237 0.955 2.0e-002 6.1e-003 2 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0763 0.992 4.2e-003 1.2e-005 3 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 2.3e-004 4.2e-005 4 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0001 1.000 2.5e-004 1.3e-005 5 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 2.4e-004 4.4e-005 6 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0001 1.000 2.6e-004 1.3e-005 7 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 2.5e-004 4.6e-005 8 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0001 1.000 2.7e-004 1.4e-005 9 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 2.7e-004 4.9e-005 10 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0002 1.000 2.9e-004 1.5e-005 11 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 2.8e-004 5.2e-005 12 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0002 1.000 3.0e-004 1.5e-005 13 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.0e-004 5.5e-005 14 1.0051e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0002 1.000 3.2e-004 1.6e-005 15 1.0050e-001 -2.6448e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.2e-004 5.8e-005 16 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0002 1.000 3.4e-004 1.7e-005 17 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.3e-004 6.1e-005 18 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0002 1.000 3.6e-004 1.8e-005 19 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.5e-004 6.4e-005 20 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0002 1.000 3.8e-004 1.9e-005 21 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.7e-004 6.8e-005 22 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0002 1.000 4.0e-004 2.0e-005 23 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0000 1.000 3.9e-004 7.1e-005 24 1.0050e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0002 1.000 4.2e-004 2.1e-005 25 1.0049e-001 -2.6449e+000 5.9323e+000 1.00e-001 0.0000 1.000 4.1e-004 7.5e-005 26 1.0049e-001 -2.6450e+000 5.9323e+000 1.00e-001 0.0002 1.000 4.4e-004 2.2e-005 27 1.0049e-001 -2.6450e+000 5.9323e+000 1.00e-001 0.0000 1.000 4.3e-004 7.9e-005 28 1.0049e-001 -2.6450e+000 5.9323e+000 1.00e-001 0.0002 1.000 4.7e-004 2.4e-005 29 1.0049e-001 -2.6450e+000 5.9323e+000 1.00e-001 0.0000 1.000 4.6e-004 8.4e-005 30 1.0049e-001 -2.6450e+000 5.9323e+000 1.00e-001 0.0003 1.000 4.9e-004 2.5e-005 Best point: x' = 1.0048941714572200e-001 -2.6450129753155140e+000. Best value: uvw(x) = 5.9322560957108030e+000. Step count: 30 Trust-Region passes. Stopped by: iteration limit reached. Flop count: 9403 total--average 313 per step. ------------------------ BFGS Quasi-Newton ------------------------ EDU> x0 = [0.2;-1.0]; bfgs BFGS/Armijo/Skipping minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) e_1 e_2 lambda 0 2.0000e-001 -1.0000e+000 6.6116e+000 1 1.2058e+000 -1.0991e+000 4.6750e+000 5.0291e+000 2.0372e+000 1.000000 2 1.5270e+000 -3.3544e-001 2.0869e+000 6.9480e-001 8.4419e-001 1.000000 3 2.0648e+000 1.4455e-001 1.2219e+000 1.4309e+000 9.4692e-001 1.000000 4 2.4157e+000 4.4172e-001 1.1453e+000 2.0559e+000 1.5017e+000 1.000000 5 2.3368e+000 3.1853e-001 1.0817e+000 2.7888e-001 9.1615e-001 1.000000 6 2.4168e+000 3.3620e-001 1.0561e+000 5.5458e-002 7.1801e-001 1.000000 7 2.6808e+000 4.0596e-001 1.0120e+000 2.0751e-001 1.8403e-001 1.000000 8 2.8181e+000 4.5427e-001 1.0033e+000 1.1898e-001 1.5279e-001 1.000000 9 2.9272e+000 4.8400e-001 1.0005e+000 6.5463e-002 8.0217e-002 1.000000 10 2.9770e+000 4.9397e-001 1.0000e+000 2.0590e-002 7.0090e-003 1.000000 11 2.9991e+000 5.0028e-001 1.0000e+000 1.2770e-002 8.7811e-003 1.000000 12 3.0001e+000 4.9995e-001 1.0000e+000 6.4623e-004 1.1964e-003 1.000000 13 3.0000e+000 5.0000e-001 1.0000e+000 9.2091e-005 5.6502e-007 1.000000 14 3.0000e+000 5.0000e-001 1.0000e+000 1.1014e-006 2.0075e-008 1.000000 Best point: x' = 2.9999999419353460e+000 4.9999998514683930e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 14 BFGS quasi-Newton steps. Stopped by: e1 < eta1. Flop count: 2600 total--average 186 per step. EDU> x0 = [1.0;0.8]; bfgs BFGS/Armijo/Skipping minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) e_1 e_2 lambda 0 1.0000e+000 8.0000e-001 5.9144e+000 1 1.3353e+000 -6.2483e-001 2.7199e+000 1.7810e+000 4.8425e-001 1.000000 2 1.4834e+000 -3.9395e-001 2.2102e+000 3.6950e-001 7.8242e-001 1.000000 3 2.5586e+000 6.7199e-001 1.9320e+000 2.7058e+000 2.6169e+000 0.729000 4 2.0963e+000 -8.9342e-002 1.4605e+000 1.1330e+000 2.2518e-001 1.000000 5 2.2191e+000 6.0761e-002 1.2540e+000 1.6801e+000 1.8318e-001 1.000000 6 2.6467e+000 5.5994e-001 1.2481e+000 8.2155e+000 1.7178e+000 1.000000 7 2.4118e+000 2.2971e-001 1.0940e+000 5.8976e-001 1.6977e-001 1.000000 8 2.5047e+000 3.1116e-001 1.0446e+000 3.5458e-001 1.3136e-001 1.000000 9 2.7343e+000 4.7258e-001 1.0257e+000 5.1877e-001 7.7042e-001 1.000000 10 2.6817e+000 4.0969e-001 1.0118e+000 1.3308e-001 2.2601e-001 1.000000 11 2.7396e+000 4.3022e-001 1.0074e+000 5.0104e-002 2.0352e-001 1.000000 12 2.8984e+000 4.7908e-001 1.0012e+000 1.1359e-001 1.3973e-001 1.000000 13 2.9552e+000 4.8981e-001 1.0002e+000 2.2386e-002 4.1587e-002 1.000000 14 2.9912e+000 4.9809e-001 1.0000e+000 1.6906e-002 9.0154e-003 1.000000 15 2.9991e+000 4.9977e-001 1.0000e+000 3.3714e-003 4.9816e-004 1.000000 16 3.0000e+000 5.0001e-001 1.0000e+000 4.8204e-004 1.1081e-004 1.000000 17 3.0000e+000 5.0000e-001 1.0000e+000 2.2147e-005 2.4136e-005 1.000000 18 3.0000e+000 5.0000e-001 1.0000e+000 2.3698e-006 7.0860e-009 1.000000 19 3.0000e+000 5.0000e-001 1.0000e+000 5.8253e-009 1.8612e-011 1.000000 Best point: x' = 3.0000000000456810e+000 5.0000000001152100e-001. Best value: uvw(x) = 1.0000000000000000e+000. Step count: 19 BFGS quasi-Newton steps. Stopped by: e1 < eta1. Flop count: 3620 total--average 191 per step. EDU> x0 = [0.1;-2.6]; bfgs BFGS/Armijo/Skipping minimization of function "uvw", using gradient "uvwd": k x_k(1) x_k(2) f(x_k) e_1 e_2 lambda 0 1.0000e-001 -2.6000e+000 5.9374e+000 1 1.0975e-001 -2.6009e+000 5.9359e+000 9.7503e-002 9.7854e-002 0.027813 2 1.0577e-001 -2.5958e+000 5.9318e+000 3.6312e-002 8.5377e-003 1.000000 3 1.0612e-001 -2.5924e+000 5.9317e+000 3.3375e-003 8.5841e-003 1.000000 3 ** Note: s'y is very small. Hessian update skipped. 4 1.0652e-001 -2.5887e+000 5.9316e+000 3.8278e-003 9.1630e-003 1.000000 4 ** Note: s'y is very small. Hessian update skipped. 5 1.0696e-001 -2.5848e+000 5.9315e+000 4.1163e-003 9.7884e-003 1.000000 5 ** Note: s'y is very small. Hessian update skipped. 6 1.0744e-001 -2.5806e+000 5.9314e+000 4.4250e-003 1.0456e-002 1.000000 6 ** Note: s'y is very small. Hessian update skipped. 7 1.0795e-001 -2.5760e+000 5.9313e+000 4.7588e-003 1.1169e-002 1.000000 7 ** Note: s'y is very small. Hessian update skipped. 8 1.0850e-001 -2.5711e+000 5.9311e+000 5.1202e-003 1.1930e-002 1.000000 8 ** Note: s'y is very small. Hessian update skipped. 9 1.0910e-001 -2.5659e+000 5.9310e+000 5.5117e-003 1.2741e-002 1.000000 9 ** Note: s'y is very small. Hessian update skipped. 10 1.0975e-001 -2.5602e+000 5.9308e+000 5.9362e-003 1.3606e-002 1.000000 10 ** Note: s'y is very small. Hessian update skipped. 11 1.1045e-001 -2.5541e+000 5.9305e+000 6.3967e-003 1.4526e-002 1.000000 11 ** Note: s'y is very small. Hessian update skipped. 12 1.1121e-001 -2.5475e+000 5.9303e+000 6.8967e-003 1.5505e-002 1.000000 12 ** Note: s'y is very small. Hessian update skipped. 13 1.1204e-001 -2.5405e+000 5.9300e+000 7.4398e-003 1.6545e-002 1.000000 13 ** Note: s'y is very small. Hessian update skipped. 14 1.1294e-001 -2.5328e+000 5.9296e+000 8.0303e-003 1.7648e-002 1.000000 14 ** Note: s'y is very small. Hessian update skipped. 15 1.1392e-001 -2.5246e+000 5.9292e+000 8.6726e-003 1.8816e-002 1.000000 15 ** Note: s'y is very small. Hessian update skipped. 16 1.1498e-001 -2.5157e+000 5.9287e+000 9.3715e-003 2.0050e-002 1.000000 16 ** Note: s'y is very small. Hessian update skipped. 17 1.1615e-001 -2.5061e+000 5.9281e+000 1.0132e-002 2.1349e-002 1.000000 17 ** Note: s'y is very small. Hessian update skipped. 18 1.1742e-001 -2.4958e+000 5.9274e+000 1.0961e-002 2.2712e-002 1.000000 18 ** Note: s'y is very small. Hessian update skipped. 19 1.1881e-001 -2.4846e+000 5.9266e+000 1.1863e-002 2.4136e-002 1.000000 19 ** Note: s'y is very small. Hessian update skipped. 20 1.2034e-001 -2.4725e+000 5.9256e+000 1.2845e-002 2.5615e-002 1.000000 20 ** Note: s'y is very small. Hessian update skipped. 21 1.2201e-001 -2.4594e+000 5.9245e+000 1.3912e-002 2.7140e-002 1.000000 21 ** Note: s'y is very small. Hessian update skipped. 22 1.2385e-001 -2.4452e+000 5.9232e+000 1.5073e-002 2.8698e-002 1.000000 22 ** Note: s'y is very small. Hessian update skipped. 23 1.2588e-001 -2.4298e+000 5.9217e+000 1.6332e-002 3.0272e-002 1.000000 23 ** Note: s'y is very small. Hessian update skipped. 24 1.2810e-001 -2.4132e+000 5.9198e+000 1.7694e-002 3.1838e-002 1.000000 24 ** Note: s'y is very small. Hessian update skipped. 25 1.3056e-001 -2.3952e+000 5.9176e+000 1.9164e-002 3.3365e-002 1.000000 25 ** Note: s'y is very small. Hessian update skipped. 26 1.3327e-001 -2.3758e+000 5.9150e+000 2.0744e-002 3.4812e-002 1.000000 26 ** Note: s'y is very small. Hessian update skipped. 27 1.3626e-001 -2.3548e+000 5.9120e+000 2.2432e-002 3.6130e-002 1.000000 27 ** Note: s'y is very small. Hessian update skipped. 28 1.3956e-001 -2.3321e+000 5.9083e+000 2.4223e-002 3.7258e-002 1.000000 28 ** Note: s'y is very small. Hessian update skipped. 29 1.4320e-001 -2.3076e+000 5.9040e+000 2.6109e-002 3.8124e-002 1.000000 29 ** Note: s'y is very small. Hessian update skipped. 30 1.4722e-001 -2.2813e+000 5.8989e+000 2.8071e-002 3.8648e-002 1.000000 30 ** Note: s'y is very small. Hessian update skipped. 31 1.5165e-001 -2.2532e+000 5.8929e+000 3.0087e-002 3.8739e-002 1.000000 31 ** Note: s'y is very small. Hessian update skipped. 32 1.5652e-001 -2.2230e+000 5.8858e+000 3.2122e-002 3.8306e-002 1.000000 32 ** Note: s'y is very small. Hessian update skipped. 33 1.6186e-001 -2.1910e+000 5.8775e+000 3.4137e-002 3.7261e-002 1.000000 33 ** Note: s'y is very small. Hessian update skipped. 34 1.6771e-001 -2.1571e+000 5.8679e+000 3.6082e-002 3.5530e-002 1.000000 34 ** Note: s'y is very small. Hessian update skipped. 35 1.7406e-001 -2.1215e+000 5.8568e+000 3.7904e-002 3.8551e-002 1.000000 35 ** Note: s'y is very small. Hessian update skipped. 36 1.8095e-001 -2.0844e+000 5.8440e+000 3.9545e-002 4.5056e-002 1.000000 36 ** Note: s'y is very small. Hessian update skipped. 37 1.8836e-001 -2.0459e+000 5.8296e+000 4.0954e-002 5.2337e-002 1.000000 37 ** Note: s'y is very small. Hessian update skipped. 38 1.9628e-001 -2.0063e+000 5.8134e+000 4.2086e-002 6.0376e-002 1.000000 38 ** Note: s'y is very small. Hessian update skipped. 39 2.0471e-001 -1.9660e+000 5.7954e+000 4.2911e-002 6.9124e-002 1.000000 39 ** Note: s'y is very small. Hessian update skipped. 40 2.1359e-001 -1.9253e+000 5.7756e+000 4.3414e-002 7.8514e-002 1.000000 40 ** Note: s'y is very small. Hessian update skipped. 41 2.2291e-001 -1.8845e+000 5.7541e+000 4.3601e-002 8.8459e-002 1.000000 41 ** Note: s'y is very small. Hessian update skipped. 42 2.3260e-001 -1.8439e+000 5.7310e+000 4.3493e-002 9.8863e-002 1.000000 42 ** Note: s'y is very small. Hessian update skipped. 43 2.4263e-001 -1.8038e+000 5.7063e+000 4.3123e-002 1.0963e-001 1.000000 43 ** Note: s'y is very small. Hessian update skipped. 44 2.5295e-001 -1.7644e+000 5.6802e+000 4.2533e-002 1.2068e-001 1.000000 44 ** Note: s'y is very small. Hessian update skipped. 45 2.6352e-001 -1.7259e+000 5.6527e+000 4.1768e-002 1.3193e-001 1.000000 45 ** Note: s'y is very small. Hessian update skipped. 46 2.7429e-001 -1.6883e+000 5.6240e+000 4.0873e-002 1.4332e-001 1.000000 46 ** Note: s'y is very small. Hessian update skipped. 47 2.8523e-001 -1.6518e+000 5.5943e+000 3.9886e-002 1.5480e-001 1.000000 47 ** Note: s'y is very small. Hessian update skipped. 48 2.9631e-001 -1.6164e+000 5.5636e+000 3.8843e-002 1.6634e-001 1.000000 48 ** Note: s'y is very small. Hessian update skipped. 49 3.0750e-001 -1.5821e+000 5.5320e+000 3.7770e-002 1.7793e-001 1.000000 49 ** Note: s'y is very small. Hessian update skipped. 50 3.1878e-001 -1.5489e+000 5.4996e+000 3.6690e-002 1.8953e-001 1.000000 50 ** Note: s'y is very small. Hessian update skipped. 51 3.3013e-001 -1.5167e+000 5.4665e+000 3.5619e-002 2.0116e-001 1.000000 51 ** Note: s'y is very small. Hessian update skipped. 52 3.4155e-001 -1.4855e+000 5.4327e+000 3.4569e-002 2.1280e-001 1.000000 52 ** Note: s'y is very small. Hessian update skipped. 53 3.5300e-001 -1.4552e+000 5.3984e+000 3.3548e-002 2.2447e-001 1.000000 53 ** Note: s'y is very small. Hessian update skipped. 54 3.6450e-001 -1.4258e+000 5.3636e+000 3.2562e-002 2.3616e-001 1.000000 54 ** Note: s'y is very small. Hessian update skipped. 55 3.7602e-001 -1.3971e+000 5.3284e+000 3.1613e-002 2.4788e-001 1.000000 55 ** Note: s'y is very small. Hessian update skipped. 56 3.8757e-001 -1.3692e+000 5.2927e+000 3.0705e-002 2.5964e-001 1.000000 56 ** Note: s'y is very small. Hessian update skipped. 57 3.9913e-001 -1.3420e+000 5.2567e+000 2.9837e-002 2.7145e-001 1.000000 57 ** Note: s'y is very small. Hessian update skipped. 58 4.1071e-001 -1.3154e+000 5.2204e+000 2.9010e-002 2.8332e-001 1.000000 58 ** Note: s'y is very small. Hessian update skipped. 59 4.2230e-001 -1.2893e+000 5.1837e+000 2.8223e-002 2.9526e-001 1.000000 59 ** Note: s'y is very small. Hessian update skipped. 60 4.3390e-001 -1.2637e+000 5.1468e+000 2.7475e-002 3.0728e-001 1.000000 60 ** Note: s'y is very small. Hessian update skipped. 61 4.4552e-001 -1.2385e+000 5.1097e+000 2.6765e-002 3.1938e-001 1.000000 61 ** Note: s'y is very small. Hessian update skipped. 62 4.5714e-001 -1.2136e+000 5.0723e+000 2.6092e-002 3.3159e-001 1.000000 62 ** Note: s'y is very small. Hessian update skipped. 63 4.6878e-001 -1.1891e+000 5.0347e+000 2.5455e-002 3.4392e-001 1.000000 63 ** Note: s'y is very small. Hessian update skipped. 64 4.8043e-001 -1.1648e+000 4.9969e+000 2.4853e-002 3.5638e-001 1.000000 64 ** Note: s'y is very small. Hessian update skipped. 65 4.9210e-001 -1.1406e+000 4.9590e+000 2.4284e-002 3.6898e-001 1.000000 65 ** Note: s'y is very small. Hessian update skipped. 66 5.0378e-001 -1.1166e+000 4.9208e+000 2.3749e-002 3.8174e-001 1.000000 66 ** Note: s'y is very small. Hessian update skipped. 67 5.1549e-001 -1.0925e+000 4.8824e+000 2.3245e-002 3.9467e-001 1.000000 67 ** Note: s'y is very small. Hessian update skipped. 68 5.2723e-001 -1.0685e+000 4.8439e+000 2.2774e-002 4.0781e-001 1.000000 68 ** Note: s'y is very small. Hessian update skipped. 69 5.3901e-001 -1.0442e+000 4.8051e+000 2.2672e-002 4.2117e-001 1.000000 69 ** Note: s'y is very small. Hessian update skipped. 70 5.5083e-001 -1.0198e+000 4.7661e+000 2.3424e-002 4.3478e-001 1.000000 70 ** Note: s'y is very small. Hessian update skipped. 71 5.6270e-001 -9.9498e-001 4.7269e+000 2.4323e-002 4.4866e-001 1.000000 71 ** Note: s'y is very small. Hessian update skipped. 72 5.7463e-001 -9.6971e-001 4.6874e+000 2.5396e-002 4.6285e-001 1.000000 72 ** Note: s'y is very small. Hessian update skipped. 73 5.8664e-001 -9.4384e-001 4.6476e+000 2.6681e-002 4.7739e-001 1.000000 73 ** Note: s'y is very small. Hessian update skipped. 74 5.9874e-001 -9.1720e-001 4.6074e+000 2.8226e-002 4.9231e-001 1.000000 74 ** Note: s'y is very small. Hessian update skipped. 75 6.1095e-001 -8.8960e-001 4.5667e+000 3.0091e-002 5.0768e-001 1.000000 75 ** Note: s'y is very small. Hessian update skipped. 76 6.2329e-001 -8.6081e-001 4.5256e+000 3.2358e-002 5.2354e-001 1.000000 76 ** Note: s'y is very small. Hessian update skipped. 77 6.3579e-001 -8.3057e-001 4.4837e+000 3.5131e-002 5.3997e-001 1.000000 77 ** Note: s'y is very small. Hessian update skipped. 78 6.4848e-001 -7.9855e-001 4.4410e+000 3.8549e-002 5.5704e-001 1.000000 78 ** Note: s'y is very small. Hessian update skipped. 79 6.6139e-001 -7.6438e-001 4.3973e+000 4.2793e-002 5.7485e-001 1.000000 79 ** Note: s'y is very small. Hessian update skipped. 80 6.7458e-001 -7.2761e-001 4.3524e+000 4.8101e-002 5.9350e-001 1.000000 80 ** Note: s'y is very small. Hessian update skipped. 81 6.8809e-001 -6.8775e-001 4.3058e+000 5.4783e-002 6.1311e-001 1.000000 81 ** Note: s'y is very small. Hessian update skipped. 82 7.0197e-001 -6.4427e-001 4.2571e+000 6.3229e-002 6.3381e-001 1.000000 82 ** Note: s'y is very small. Hessian update skipped. 83 7.1627e-001 -5.9665e-001 4.2061e+000 7.3912e-002 6.5574e-001 1.000000 83 ** Note: s'y is very small. Hessian update skipped. 84 7.3102e-001 -5.4453e-001 4.1522e+000 8.7358e-002 6.7899e-001 1.000000 84 ** Note: s'y is very small. Hessian update skipped. 85 7.4624e-001 -4.8787e-001 4.0953e+000 1.0405e-001 7.0359e-001 1.000000 85 ** Note: s'y is very small. Hessian update skipped. 86 7.6185e-001 -4.2727e-001 4.0358e+000 1.2422e-001 7.2933e-001 1.000000 86 ** Note: s'y is very small. Hessian update skipped. 87 7.7770e-001 -3.6426e-001 3.9750e+000 1.4747e-001 7.5570e-001 1.000000 88 9.6194e-001 3.6637e-001 3.8634e+000 2.0058e+000 8.5091e-001 0.020276 89 8.6882e-001 -9.9419e-002 3.6547e+000 1.2714e+000 8.8721e-001 1.000000 90 9.1351e-001 -8.4437e-003 3.5253e+000 9.1507e-001 9.4107e-001 1.000000 91 1.1829e+000 3.7854e-001 3.1915e+000 4.5831e+001 1.0968e+000 1.000000 92 1.2226e+000 2.4432e-001 2.7798e+000 3.5456e-001 1.2621e+000 1.000000 93 1.7372e+000 -2.0098e-002 1.5629e+000 1.0823e+000 1.2487e+000 1.000000 94 2.0164e+000 -2.1456e-004 1.3460e+000 9.8932e-001 4.8727e-001 1.000000 95 2.2609e+000 1.5584e-001 1.1539e+000 7.2736e+002 1.3606e-001 1.000000 96 2.5936e+000 4.4728e-001 1.0523e+000 1.8700e+000 1.0274e+000 1.000000 97 2.5873e+000 3.6391e-001 1.0238e+000 1.8640e-001 1.6805e-001 1.000000 98 2.6824e+000 4.0632e-001 1.0118e+000 1.1655e-001 1.8045e-001 1.000000 99 2.8661e+000 4.7488e-001 1.0026e+000 1.6874e-001 2.2732e-001 1.000000 100 2.9241e+000 4.8214e-001 1.0005e+000 2.0219e-002 6.5412e-002 1.000000 Best point: x' = 2.9240808508338260e+000 4.8214009405540420e-001. Best value: uvw(x) = 1.0005279195415750e+000. Step count: 100 BFGS quasi-Newton steps. Stopped by: iteration limit reached. Flop count: 16682 total--average 167 per step.