我正在尝试解决以下问题：我正在生长的器官有很多（〜80000）表面斑块。我测量了其随时间变化的每个区域（18个时间点），并希望拟合一条增长曲线（双逻辑模型，例如，仅是两个逻辑函数bcs的总和。有两个“增长突增”发生在观察期）。
我有框式约束来确保指数项不爆炸，而线性约束则是一个增长突增必须在另一个之后发生。另外，为了在拟合参数中实现某种类型的空间连续性，我在目标函数（最小二乘）上添加了一个惩罚项，其为相邻面片（某些）参数之间的差的平方和，因此个体模型拟合不再是独立的。
我有整个过程的梯度和粗麻布，并且我以越来越细的比例来解决它，从总表面积开始，细分，映射适合每个补丁的全局模型的参数，再次运行求解器，细分...直到获得所需的分辨率。
因此，使用IPOPT进行优化是可行的，但速度非常慢，并且由于我在所有与优化理论有关的事情上都有些菜鸟，所以我想知道我是否在设置中进行了非常愚蠢的操作。我将ma86用作针对在具有256G RAM和56核以及metis重新排序的计算机上运行的openBLAS编译的线性求解器。我使用的其他设置是：
% nlp scaling
solv_options.ipopt.nlp_scaling_method = 'gradient-based';
solv_options.ipopt.nlp_scaling_max_gradient = 1;
solv_options.ipopt.nlp_scaling_min_value = 1e-16;
solv_options.ipopt.bound_mult_init_method='constant';
% Barrier Parameter
solv_options.ipopt.mu_strategy = 'adaptive';
solv_options.ipopt.mu_oracle = 'quality-function';
solv_options.ipopt.fixed_mu_oracle = 'average_compl';
solv_options.ipopt.adaptive_mu_globalization = 'kkt-error';
solv_options.ipopt.corrector_type = 'affine';
% linear solver
solv_options.ipopt.max_soc=0;
solv_options.ipopt.accept_every_trial_step='yes';
solv_options.ipopt.linear_system_scaling = 'none';
solv_options.ipopt.neg_curv_test_tol = 0;
solv_options.ipopt.neg_curv_test_reg = 'yes';
solv_options.ipopt.max_refinement_steps=0;
solv_options.ipopt.min_refinement_steps=0;
% ma86 settings
solv_options.ipopt.linear_solver='ma86';
solv_options.ipopt.ma86_order='auto';
solv_options.ipopt.ma86_scaling='mc64';
solv_options.ipopt.ma86_small=1e-10;
solv_options.ipopt.ma86_static=1;
solv_options.ipopt.recalc_y='yes';
这给了我这样的东西：
This is Ipopt version 3.12, running with linear solver ma86.
Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 2560
Number of nonzeros in Lagrangian Hessian.............: 112280
Total number of variables............................: 8960
variables with only lower bounds: 2560
variables with lower and upper bounds: 3840
variables with only upper bounds: 2560
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 1280
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 1280
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 9.8260736e-01 0.00e+00 1.19e-02 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 9.6288666e-01 0.00e+00 1.24e-02 -4.5 1.14e-02 0.0 9.91e-01 1.00e+00f 1
2 9.1582880e-01 0.00e+00 1.16e-02 -4.4 2.72e-02 -0.5 1.00e+00 1.00e+00f 1
3 8.2635857e-01 0.00e+00 1.01e-02 -4.6 1.39e-01 -1.0 9.99e-01 1.00e+00f 1
4 7.8943781e-01 0.00e+00 9.40e-03 -4.9 2.70e-02 -0.5 1.00e+00 1.00e+00f 1
5 7.2123624e-01 0.00e+00 8.12e-03 -5.3 8.70e-02 -1.0 1.00e+00 1.00e+00f 1
6 6.9535003e-01 0.00e+00 7.56e-03 -6.1 2.20e-02 -0.6 1.00e+00 9.06e-01f 1
7 6.6635914e-01 0.00e+00 7.00e-03 -6.6 6.21e-02 -1.1 1.00e+00 5.40e-01f 1
8 6.5683787e-01 0.00e+00 6.78e-03 -7.6 2.14e-02 -0.6 1.00e+00 3.81e-01f 1
9 6.4238130e-01 0.00e+00 6.53e-03 -7.7 1.53e-01 -1.1 1.00e+00 2.90e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 6.3440625e-01 0.00e+00 6.33e-03 -8.7 2.20e-02 -0.7 1.00e+00 3.30e-01f 1
11 6.2431009e-01 0.00e+00 6.16e-03 -8.3 3.08e-01 -1.2 1.00e+00 2.04e-01f 1
12 6.1872460e-01 0.00e+00 6.05e-03 -8.8 2.29e-02 -0.7 1.00e+00 2.32e-01f 1
13 6.0753815e-01 0.00e+00 5.86e-03 -8.9 2.73e-01 -1.2 1.00e+00 2.31e-01f 1
14 6.0575477e-01 0.00e+00 5.82e-03 -9.9 2.60e-02 -0.8 1.00e+00 7.44e-02f 1
15 6.0089103e-01 0.00e+00 5.71e-03 -11.0 1.11e-02 -0.4 1.00e+00 4.48e-01f 1
16 5.9426852e-01 0.00e+00 5.58e-03 -11.0 3.14e-02 -0.8 1.00e+00 2.68e-01f 1
17 5.9175418e-01 0.00e+00 5.52e-03 -11.0 1.17e-02 -0.4 1.00e+00 2.26e-01f 1
18 5.8756155e-01 0.00e+00 5.44e-03 -11.0 3.97e-02 -0.9 1.00e+00 1.65e-01f 1
19 5.8651702e-01 0.00e+00 5.42e-03 -9.5 1.26e-02 -0.5 1.00e+00 8.89e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 5.8278151e-01 0.00e+00 5.34e-03 -10.3 5.18e-02 -0.9 1.00e+00 1.40e-01f 1
21 5.8100614e-01 0.00e+00 5.30e-03 -11.0 1.37e-02 -0.5 1.00e+00 1.42e-01f 1
22 5.7827149e-01 0.00e+00 5.25e-03 -11.0 7.12e-02 -1.0 1.00e+00 9.77e-02f 1
23 5.7564914e-01 0.00e+00 5.19e-03 -9.4 1.52e-02 -0.6 1.00e+00 1.97e-01f 1
24 5.7340095e-01 0.00e+00 5.15e-03 -10.0 1.06e-01 -1.0 1.00e+00 7.66e-02f 1
25 5.7134734e-01 0.00e+00 5.10e-03 -11.0 1.78e-02 -0.6 1.00e+00 1.45e-01f 1
26 5.6897098e-01 0.00e+00 5.06e-03 -11.0 1.82e-01 -1.1 1.00e+00 7.65e-02f 1
27 5.6722484e-01 0.00e+00 5.02e-03 -11.0 2.11e-02 -0.7 1.00e+00 1.16e-01f 1
28 5.6402838e-01 0.00e+00 5.25e-03 -11.0 3.29e-01 -1.1 1.00e+00 9.57e-02f 1
29 5.6299118e-01 0.00e+00 5.26e-03 -10.5 2.38e-02 -0.7 1.00e+00 6.53e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 5.5753178e-01 0.00e+00 5.63e-03 -11.0 1.38e-01 -1.2 1.00e+00 1.62e-01f 1
31 5.5730217e-01 0.00e+00 5.63e-03 -11.0 2.37e-02 -0.8 1.00e+00 1.38e-02f 1
32 5.5363398e-01 0.00e+00 5.71e-03 -11.0 8.55e-02 -1.2 1.00e+00 1.06e-01f 1
33 5.5223091e-01 0.00e+00 5.70e-03 -11.0 2.43e-02 -0.8 1.00e+00 7.99e-02f 1
34 5.5163441e-01 0.00e+00 5.70e-03 -9.9 1.30e-01 -1.3 1.00e+00 1.65e-02f 1
35 5.4699694e-01 0.00e+00 5.67e-03 -10.9 2.56e-02 -0.9 1.00e+00 2.48e-01f 1
36 5.4559780e-01 0.00e+00 5.67e-03 -11.0 2.30e-01 -1.3 1.00e+00 3.71e-02f 1
37 5.4248376e-01 0.00e+00 5.63e-03 -11.0 2.58e-02 -0.9 1.00e+00 1.60e-01f 1
38 5.3955718e-01 0.00e+00 5.63e-03 -10.7 6.78e-01 -1.4 1.00e+00 6.97e-02f 1
39 5.3606672e-01 0.00e+00 5.57e-03 -10.9 2.79e-02 -1.0 1.00e+00 1.73e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 5.3481638e-01 0.00e+00 5.55e-03 -11.0 1.32e-02 -0.5 1.00e+00 1.33e-01f 1
41 5.3248177e-01 0.00e+00 5.50e-03 -11.0 3.23e-02 -1.0 1.00e+00 1.10e-01f 1
42 5.3143109e-01 0.00e+00 5.48e-03 -10.4 1.37e-02 -0.6 1.00e+00 1.05e-01f 1
43 5.2975978e-01 0.00e+00 5.45e-03 -11.0 3.92e-02 -1.1 1.00e+00 7.50e-02f 1
44 5.2855042e-01 0.00e+00 5.42e-03 -11.0 1.50e-02 -0.6 1.00e+00 1.13e-01f 1
45 5.2670676e-01 0.00e+00 5.38e-03 -11.0 4.80e-02 -1.1 1.00e+00 7.85e-02f 1
46 5.2428812e-01 0.00e+00 5.31e-03 -11.0 1.64e-02 -0.7 1.00e+00 2.12e-01f 1
47 5.2221881e-01 0.00e+00 5.27e-03 -11.0 5.84e-02 -1.2 1.00e+00 8.45e-02f 1
48 5.2084516e-01 0.00e+00 5.23e-03 -10.8 1.79e-02 -0.8 1.00e+00 1.14e-01f 1
49 5.1928549e-01 0.00e+00 5.19e-03 -11.0 7.06e-02 -1.2 1.00e+00 6.06e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 5.1787195e-01 0.00e+00 5.15e-03 -11.0 1.95e-02 -0.8 1.00e+00 1.10e-01f 1
51 5.1639782e-01 0.00e+00 5.12e-03 -10.9 8.49e-02 -1.3 1.00e+00 5.45e-02f 1
52 5.1606363e-01 0.00e+00 5.11e-03 -11.0 2.13e-02 -0.9 1.00e+00 2.45e-02f 1
53 5.1178863e-01 0.00e+00 5.01e-03 -11.0 1.04e-01 -1.3 1.00e+00 1.50e-01f 1
54 5.1173718e-01 0.00e+00 5.01e-03 -11.0 2.33e-02 -0.9 1.00e+00 3.61e-03f 1
55 5.0944130e-01 0.00e+00 4.96e-03 -11.0 1.40e-01 -1.4 1.00e+00 7.70e-02f 1
56 5.0727659e-01 0.00e+00 4.89e-03 -11.0 2.55e-02 -1.0 1.00e+00 1.43e-01f 1
57 5.0638483e-01 0.00e+00 4.85e-03 -11.0 1.11e-02 -0.5 1.00e+00 1.29e-01f 1
58 5.0426908e-01 0.00e+00 4.78e-03 -11.0 2.79e-02 -1.0 1.00e+00 1.32e-01f 1
59 5.0333858e-01 0.00e+00 4.74e-03 -11.0 1.22e-02 -0.6 1.00e+00 1.26e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 5.0161958e-01 0.00e+00 4.69e-03 -11.0 3.05e-02 -1.1 1.00e+00 1.02e-01f 1
61 5.0037437e-01 0.00e+00 4.64e-03 -11.0 1.34e-02 -0.6 1.00e+00 1.58e-01f 1
62 4.9971029e-01 0.00e+00 4.62e-03 -11.0 3.34e-02 -1.1 1.00e+00 3.72e-02f 1
63 4.9914235e-01 0.00e+00 4.59e-03 -11.0 1.48e-02 -0.7 1.00e+00 6.69e-02f 1
64 4.9664256e-01 0.00e+00 4.51e-03 -11.0 3.70e-02 -1.2 1.00e+00 1.32e-01f 1
65 4.9621567e-01 0.00e+00 4.50e-03 -11.0 1.62e-02 -0.7 1.00e+00 4.72e-02f 1
66 4.9453149e-01 0.00e+00 4.44e-03 -11.0 4.19e-02 -1.2 1.00e+00 8.39e-02f 1
67 4.9304626e-01 0.00e+00 4.38e-03 -11.0 1.79e-02 -0.8 1.00e+00 1.53e-01f 1
68 4.9163087e-01 0.00e+00 4.34e-03 -11.0 6.89e-02 -1.3 1.00e+00 6.69e-02f 1
69 4.9031174e-01 0.00e+00 4.28e-03 -11.0 1.97e-02 -0.8 1.00e+00 1.28e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
70 4.8795240e-01 0.00e+00 4.22e-03 -8.8 2.01e-01 -1.3 9.38e-01 1.04e-01f 1
71 4.8721723e-01 0.00e+00 4.18e-03 -9.8 2.16e-02 -0.9 1.00e+00 6.73e-02f 1
72 4.8560412e-01 0.00e+00 4.10e-03 -11.0 9.08e-03 -0.5 1.00e+00 3.33e-01f 1
73 4.8395604e-01 0.00e+00 4.03e-03 -11.0 2.38e-02 -0.9 1.00e+00 1.42e-01f 1
74 4.8308417e-01 0.00e+00 3.99e-03 -11.0 9.99e-03 -0.5 1.00e+00 1.69e-01f 1
75 4.8236398e-01 0.00e+00 3.96e-03 -10.8 2.63e-02 -1.0 1.00e+00 5.83e-02f 1
76 4.7919513e-01 0.00e+00 3.79e-03 -10.9 1.11e-02 -0.6 1.00e+00 5.72e-01f 1
77 4.7844811e-01 0.00e+00 3.76e-03 -11.0 3.12e-02 -1.0 1.00e+00 5.79e-02f 1
78 4.7801338e-01 0.00e+00 3.74e-03 -11.0 1.22e-02 -0.6 1.00e+00 7.40e-02f 1
79 4.7631089e-01 0.00e+00 3.67e-03 -11.0 4.30e-02 -1.1 1.00e+00 1.23e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
80 4.7516941e-01 0.00e+00 3.61e-03 -11.0 1.35e-02 -0.7 1.00e+00 1.81e-01f 1
81 4.7405503e-01 0.00e+00 3.57e-03 -11.0 7.24e-02 -1.1 1.00e+00 7.54e-02f 1
82 4.7394863e-01 0.00e+00 3.57e-03 -11.0 1.49e-02 -0.7 1.00e+00 1.57e-02f 1
83 4.7209146e-01 0.00e+00 3.51e-03 -8.9 1.76e-01 -1.2 9.65e-01 1.15e-01f 1
84 4.7199185e-01 0.00e+00 3.50e-03 -10.1 1.66e-02 -0.8 1.00e+00 1.36e-02f 1
85 4.7051045e-01 0.00e+00 3.41e-03 -11.0 6.70e-03 -0.3 1.00e+00 4.74e-01f 1
86 4.7028360e-01 0.00e+00 3.40e-03 -11.0 1.92e-02 -0.8 1.00e+00 2.87e-02f 1
87 4.6892068e-01 0.00e+00 3.31e-03 -11.0 7.44e-03 -0.4 1.00e+00 4.02e-01f 1
88 4.6754658e-01 0.00e+00 3.25e-03 -11.0 2.37e-02 -0.9 1.00e+00 1.62e-01f 1
89 4.6723856e-01 0.00e+00 3.23e-03 -11.0 8.24e-03 -0.4 1.00e+00 8.47e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
90 4.6625331e-01 0.00e+00 3.18e-03 -11.0 3.07e-02 -0.9 1.00e+00 1.08e-01f 1
91 4.6621348e-01 0.00e+00 3.18e-03 -11.0 9.16e-03 -0.5 1.00e+00 1.01e-02f 1
92 4.6511327e-01 0.00e+00 3.17e-03 -11.0 4.12e-02 -1.0 1.00e+00 1.11e-01f 1
93 4.6363418e-01 0.00e+00 3.14e-03 -11.0 1.02e-02 -0.5 1.00e+00 3.45e-01f 1
94 4.6314545e-01 0.00e+00 3.14e-03 -11.0 6.17e-02 -1.0 1.00e+00 4.60e-02f 1
95 4.6235630e-01 0.00e+00 3.12e-03 -11.0 1.13e-02 -0.6 1.00e+00 1.70e-01f 1
96 4.6143809e-01 0.00e+00 3.11e-03 -9.7 1.03e-01 -1.1 1.00e+00 7.93e-02f 1
97 4.6069624e-01 0.00e+00 3.10e-03 -10.6 1.38e-02 -0.6 1.00e+00 1.47e-01f 1
98 4.5824023e-01 0.00e+00 3.68e-03 -8.6 3.14e-01 -1.1 8.52e-01 1.81e-01f 1
99 4.5822224e-01 0.00e+00 3.68e-03 -9.9 2.27e-02 -0.7 1.00e+00 3.30e-03f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
100 4.5747364e-01 0.00e+00 3.71e-03 -11.0 7.25e-03 -0.3 1.00e+00 3.33e-01f 1
101 4.5651156e-01 0.00e+00 3.77e-03 -11.0 2.65e-02 -0.8 1.00e+00 1.62e-01f 1
102 4.5624508e-01 0.00e+00 3.79e-03 -11.0 8.36e-03 -0.3 1.00e+00 1.09e-01f 1
103 4.5460694e-01 0.00e+00 3.91e-03 -10.5 3.10e-02 -0.8 1.00e+00 2.54e-01f 1
104 4.5415701e-01 0.00e+00 3.92e-03 -11.0 9.64e-03 -0.4 1.00e+00 1.69e-01f 1
105 4.5379967e-01 0.00e+00 3.95e-03 -11.0 3.54e-02 -0.9 1.00e+00 5.13e-02f 1
106 4.5282822e-01 0.00e+00 3.99e-03 -11.0 1.10e-02 -0.4 1.00e+00 3.33e-01f 1
107 4.5236345e-01 0.00e+00 4.03e-03 -11.0 4.03e-02 -0.9 1.00e+00 6.16e-02f 1
108 4.5158337e-01 0.00e+00 4.06e-03 -11.0 1.24e-02 -0.5 1.00e+00 2.45e-01f 1
109 4.4983066e-01 0.00e+00 4.19e-03 -8.9 4.54e-02 -1.0 1.00e+00 2.15e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
110 4.4976166e-01 0.00e+00 4.20e-03 -10.3 1.39e-02 -0.5 1.00e+00 2.01e-02f 1
111 4.4733643e-01 0.00e+00 4.34e-03 -8.3 4.72e-02 -1.0 9.30e-01 2.78e-01f 1
112 4.4674741e-01 0.00e+00 4.36e-03 -9.7 1.51e-02 -0.6 1.00e+00 1.60e-01f 1
113 4.4600496e-01 0.00e+00 4.39e-03 -8.6 4.25e-02 -1.1 1.00e+00 8.06e-02f 1
114 4.4596146e-01 0.00e+00 4.39e-03 -10.0 1.64e-02 -0.6 1.00e+00 1.09e-02f 1
115 4.4157951e-01 0.00e+00 4.49e-03 -8.4 4.50e-02 -1.1 1.00e+00 4.49e-01f 1
116 4.4137682e-01 0.00e+00 4.48e-03 -9.6 1.60e-02 -0.7 1.00e+00 4.90e-02f 1
117 4.3873388e-01 0.00e+00 4.47e-03 -7.5 3.70e-02 -1.2 9.19e-01 2.63e-01f 1
118 4.3815153e-01 0.00e+00 4.45e-03 -8.7 1.61e-02 -0.7 1.00e+00 1.33e-01f 1
119 4.3569743e-01 0.00e+00 4.41e-03 -7.5 3.98e-02 -1.2 1.00e+00 2.34e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
120 4.3444019e-01 0.00e+00 4.36e-03 -8.6 1.67e-02 -0.8 1.00e+00 2.71e-01f 1
121 4.3145745e-01 0.00e+00 4.27e-03 -7.3 4.24e-02 -1.3 1.00e+00 2.74e-01f 1
122 4.2975412e-01 0.00e+00 4.19e-03 -8.0 1.81e-02 -0.8 1.00e+00 3.55e-01f 1
123 4.2433966e-01 0.00e+00 3.98e-03 -6.9 4.56e-02 -1.3 1.00e+00 4.92e-01f 1
124 4.2414838e-01 0.00e+00 3.96e-03 -7.5 1.92e-02 -0.9 1.00e+00 4.01e-02f 1
125 4.2194620e-01 0.00e+00 3.87e-03 -6.9 4.80e-02 -1.4 1.00e+00 1.96e-01f 1
126 4.1778190e-01 0.00e+00 3.63e-03 -7.7 2.08e-02 -0.9 1.00e+00 8.34e-01f 1
127 4.1737428e-01 0.00e+00 2.94e-03 -7.1 4.72e-02 -1.4 1.00e+00 3.66e-02f 1
128 4.1315312e-01 0.00e+00 2.54e-03 -7.8 2.22e-02 -1.0 1.00e+00 8.46e-01f 1
129 4.1173197e-01 0.00e+00 2.51e-03 -7.1 6.31e-02 -1.5 1.00e+00 1.27e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
130 4.0915489e-01 0.00e+00 2.46e-03 -7.7 2.32e-02 -1.0 1.00e+00 5.13e-01f 1
131 4.0515277e-01 0.00e+00 2.38e-03 -6.9 9.97e-02 -1.5 1.00e+00 3.50e-01f 1
132 4.0343660e-01 0.00e+00 2.34e-03 -7.3 2.38e-02 -1.1 1.00e+00 3.43e-01f 1
133 3.9516682e-01 0.00e+00 2.17e-03 -6.8 1.68e-01 -1.6 1.00e+00 7.24e-01f 1
134 3.9098427e-01 0.00e+00 2.06e-03 -7.2 2.34e-02 -1.1 1.00e+00 9.07e-01f 1
135 3.9058959e-01 0.00e+00 2.05e-03 -7.0 5.50e-02 -1.6 1.00e+00 3.97e-02f 1
136 3.8628795e-01 0.00e+00 1.93e-03 -7.7 2.39e-02 -1.2 1.00e+00 9.42e-01f 1
137 3.8288703e-01 0.00e+00 1.84e-03 -7.2 6.76e-02 -1.7 1.00e+00 3.49e-01f 1
138 3.8113960e-01 0.00e+00 1.79e-03 -7.8 2.37e-02 -1.2 1.00e+00 4.02e-01f 1
139 3.7895865e-01 0.00e+00 1.74e-03 -7.3 8.98e-02 -1.7 1.00e+00 2.23e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
140 3.7630588e-01 0.00e+00 1.65e-03 -7.9 2.56e-02 -1.3 1.00e+00 6.04e-01f 1
141 3.7040736e-01 0.00e+00 2.44e-03 -7.4 4.40e-01 -1.8 1.00e+00 5.52e-01f 1
142 3.6744301e-01 0.00e+00 2.20e-03 -8.1 5.47e-02 -1.3 1.00e+00 6.87e-01f 1
143 3.6668338e-01 0.00e+00 2.11e-03 -9.7 1.27e-02 -0.9 1.00e+00 4.33e-01f 1
144 3.6563026e-01 0.00e+00 2.04e-03 -10.0 1.45e-01 -1.4 1.00e+00 2.33e-01f 1
145 3.6473497e-01 0.00e+00 1.94e-03 -11.0 1.73e-02 -1.0 1.00e+00 4.85e-01f 1
146 3.6423323e-01 0.00e+00 2.14e-03 -11.0 2.77e-01 -1.5 1.00e+00 1.00e-01f 1
147 3.6397151e-01 0.00e+00 2.15e-03 -10.1 2.02e-02 -1.0 1.00e+00 1.32e-01f 1
148 3.6196968e-01 0.00e+00 2.50e-03 -8.5 1.56e-01 -1.5 1.00e+00 3.92e-01f 1
149 3.6176499e-01 0.00e+00 2.49e-03 -9.6 1.65e-02 -1.1 1.00e+00 1.00e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
150 3.6069639e-01 0.00e+00 2.45e-03 -8.4 3.49e-02 -1.6 1.00e+00 2.18e-01f 1
151 3.6041434e-01 0.00e+00 2.43e-03 -9.4 1.63e-02 -1.1 1.00e+00 1.30e-01f 1
152 3.5921303e-01 0.00e+00 2.37e-03 -8.5 3.78e-02 -1.6 1.00e+00 2.34e-01f 1
153 3.5869485e-01 0.00e+00 2.33e-03 -9.4 1.64e-02 -1.2 1.00e+00 2.27e-01f 1
154 3.5699552e-01 0.00e+00 2.25e-03 -7.9 4.06e-02 -1.7 1.00e+00 3.20e-01f 1
155 3.5674149e-01 0.00e+00 2.23e-03 -8.7 1.77e-02 -1.2 1.00e+00 1.07e-01f 1
156 3.5471902e-01 0.00e+00 2.11e-03 -7.5 4.33e-02 -1.7 1.00e+00 3.71e-01f 1
157 3.5335745e-01 0.00e+00 1.99e-03 -8.3 1.91e-02 -1.3 1.00e+00 5.64e-01f 1
158 3.5245420e-01 0.00e+00 1.94e-03 -7.5 4.53e-02 -1.8 1.00e+00 1.67e-01f 1
159 3.5021073e-01 0.00e+00 1.73e-03 -8.3 2.05e-02 -1.3 1.00e+00 9.16e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
160 3.4610138e-01 0.00e+00 1.04e-03 -7.3 4.72e-02 -1.8 1.00e+00 7.94e-01f 1
161 3.4469412e-01 0.00e+00 9.99e-04 -8.0 2.07e-02 -1.4 1.00e+00 6.40e-01f 1
162 3.4399767e-01 0.00e+00 1.02e-03 -7.7 4.72e-02 -1.9 1.00e+00 1.42e-01f 1
163 3.4260897e-01 0.00e+00 9.60e-04 -8.1 2.22e-02 -1.4 1.00e+00 6.21e-01f 1
164 3.4129508e-01 0.00e+00 9.37e-04 -7.4 4.92e-02 -1.9 1.00e+00 2.68e-01f 1
165 3.4016827e-01 0.00e+00 9.15e-04 -8.0 2.34e-02 -1.5 1.00e+00 5.07e-01f 1
166 3.3825082e-01 0.00e+00 8.81e-04 -7.2 5.10e-02 -2.0 1.00e+00 3.98e-01f 1
167 3.3610567e-01 0.00e+00 8.39e-04 -7.7 2.44e-02 -1.5 1.00e+00 1.00e+00f 1
168 3.3460677e-01 0.00e+00 8.12e-04 -7.1 5.92e-02 -2.0 1.00e+00 3.31e-01f 1
169 3.3266040e-01 0.00e+00 7.74e-04 -7.7 2.51e-02 -1.6 1.00e+00 9.50e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
170 3.3037125e-01 0.00e+00 7.34e-04 -7.1 8.30e-02 -2.1 1.00e+00 5.31e-01f 1
171 3.2873890e-01 0.00e+00 7.02e-04 -7.7 2.53e-02 -1.6 1.00e+00 8.56e-01f 1
172 3.2622239e-01 0.00e+00 6.57e-04 -7.2 5.31e-02 -2.1 1.00e+00 6.32e-01f 1
173 3.2470308e-01 0.00e+00 6.28e-04 -7.8 2.53e-02 -1.7 1.00e+00 8.69e-01f 1
174 3.2372187e-01 0.00e+00 6.27e-04 -7.5 5.26e-02 -2.2 1.00e+00 2.63e-01f 1
175 3.2283458e-01 0.00e+00 5.92e-04 -8.2 2.60e-02 -1.7 1.00e+00 5.20e-01f 1
176 3.2183252e-01 0.00e+00 6.17e-04 -7.5 5.47e-02 -2.2 1.00e+00 2.71e-01f 1
177 3.2046827e-01 0.00e+00 5.47e-04 -8.1 2.70e-02 -1.8 1.00e+00 8.08e-01f 1
178 3.1975003e-01 0.00e+00 6.03e-04 -7.1 5.85e-02 -2.3 1.00e+00 2.04e-01f 1
179 3.1900035e-01 0.00e+00 5.19e-04 -7.6 2.77e-02 -1.8 1.00e+00 4.53e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
180 3.1615561e-01 0.00e+00 4.90e-04 -6.8 6.32e-02 -2.3 1.00e+00 8.53e-01f 1
181 3.1524761e-01 0.00e+00 4.49e-04 -7.3 2.68e-02 -1.9 1.00e+00 5.85e-01f 1
182 3.1326122e-01 0.00e+00 4.87e-04 -7.0 6.24e-02 -2.4 9.98e-01 6.26e-01f 1
183 3.1296679e-01 0.00e+00 4.09e-04 -7.7 2.63e-02 -1.9 1.00e+00 2.01e-01f 1
184 3.1055716e-01 0.00e+00 4.34e-04 -6.8 6.57e-02 -2.4 1.00e+00 8.22e-01f 1
185 3.1020674e-01 0.00e+00 3.60e-04 -7.5 2.70e-02 -2.0 1.00e+00 2.54e-01f 1
186 3.0929569e-01 0.00e+00 4.68e-04 -7.0 6.86e-02 -2.5 1.00e+00 3.18e-01f 1
187 3.0819030e-01 0.00e+00 3.23e-04 -7.8 2.94e-02 -2.0 1.00e+00 8.02e-01f 1
188 3.0763044e-01 0.00e+00 4.47e-04 -7.2 8.21e-02 -2.5 1.00e+00 2.02e-01f 1
189 3.0725472e-01 0.00e+00 3.07e-04 -8.0 3.11e-02 -2.1 1.00e+00 2.85e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
190 3.0578606e-01 0.00e+00 4.05e-04 -7.5 2.33e-01 -2.6 1.00e+00 5.11e-01f 1
191 3.0495222e-01 0.00e+00 3.43e-04 -8.1 2.91e-02 -2.2 1.00e+00 6.59e-01f 1
192 3.0413633e-01 0.00e+00 1.17e-03 -7.6 4.93e-01 -2.6 1.00e+00 2.84e-01f 1
193 3.0331078e-01 0.00e+00 9.60e-04 -7.7 3.14e-02 -2.2 1.00e+00 6.81e-01f 1
194 3.0239991e-01 0.00e+00 8.65e-04 -6.7 7.67e-02 -2.7 9.99e-01 4.00e-01f 1
195 3.0137954e-01 0.00e+00 6.77e-04 -7.5 3.36e-02 -2.3 1.00e+00 8.52e-01f 1
196 3.0056119e-01 0.00e+00 6.24e-04 -7.5 8.05e-02 -2.7 1.00e+00 3.28e-01f 1
197 3.0014178e-01 0.00e+00 5.65e-04 -8.3 3.58e-02 -2.3 1.00e+00 3.62e-01f 1
198 2.9923633e-01 0.00e+00 5.17e-04 -8.2 8.53e-02 -2.8 1.00e+00 3.59e-01f 1
199 2.9888005e-01 0.00e+00 4.75e-04 -8.9 3.83e-02 -2.4 1.00e+00 3.15e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
200 2.9848396e-01 0.00e+00 4.57e-04 -8.1 8.98e-02 -2.8 1.00e+00 1.58e-01f 1
201 2.9821853e-01 0.00e+00 4.30e-04 -8.8 4.15e-02 -2.4 1.00e+00 2.29e-01f 1
202 2.9738245e-01 0.00e+00 3.96e-04 -7.2 9.62e-02 -2.9 9.99e-01 3.39e-01f 1
203 2.9665614e-01 0.00e+00 3.36e-04 -7.8 4.41e-02 -2.5 1.00e+00 6.30e-01f 1
204 2.9578199e-01 0.00e+00 3.07e-04 -6.8 1.02e-01 -2.9 1.00e+00 3.87e-01f 1
205 2.9465429e-01 0.00e+00 2.39e-04 -7.4 4.54e-02 -2.5 1.00e+00 1.00e+00f 1
206 2.9301415e-01 0.00e+00 1.99e-04 -6.7 1.07e-01 -3.0 1.00e+00 8.01e-01f 1
207 2.9292261e-01 0.00e+00 1.94e-04 -7.3 4.47e-02 -2.6 1.00e+00 8.17e-02f 1
208 2.9132376e-01 0.00e+00 2.05e-04 -6.8 1.11e-01 -3.0 1.00e+00 7.08e-01f 1
209 2.9068030e-01 0.00e+00 1.46e-04 -7.4 4.72e-02 -2.6 1.00e+00 5.83e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
210 2.8989341e-01 0.00e+00 2.15e-04 -6.8 1.19e-01 -3.1 1.00e+00 3.71e-01f 1
211 2.8905846e-01 0.00e+00 1.25e-04 -7.4 5.00e-02 -2.7 1.00e+00 7.99e-01f 1
212 2.8817010e-01 0.00e+00 2.35e-04 -6.9 1.32e-01 -3.1 1.00e+00 4.36e-01f 1
213 2.8741077e-01 0.00e+00 1.25e-04 -7.5 5.21e-02 -2.7 1.00e+00 7.41e-01f 1
214 2.8705020e-01 0.00e+00 2.96e-04 -7.2 1.57e-01 -3.2 1.00e+00 1.65e-01f 1
215 2.8639044e-01 0.00e+00 1.29e-04 -8.0 5.54e-02 -2.8 1.00e+00 6.44e-01f 1
216 2.8567025e-01 0.00e+00 2.13e-04 -7.4 4.30e-01 -3.2 1.00e+00 3.16e-01f 1
217 2.8519078e-01 0.00e+00 1.22e-04 -8.1 6.05e-02 -2.8 1.00e+00 4.79e-01f 1
218 2.8508336e-01 0.00e+00 1.93e-04 -7.5 3.80e-01 -3.3 1.00e+00 4.58e-02f 1
219 2.8459190e-01 0.00e+00 1.16e-04 -8.3 6.70e-02 -2.9 1.00e+00 4.75e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
220 2.8382163e-01 0.00e+00 1.63e-04 -7.2 3.30e-01 -3.3 1.00e+00 3.29e-01f 1
221 2.8341130e-01 0.00e+00 1.28e-04 -7.8 7.27e-02 -2.9 1.00e+00 3.93e-01f 1
222 2.8284739e-01 0.00e+00 1.56e-04 -7.0 2.21e-01 -3.4 1.00e+00 2.45e-01f 1
223 2.8183563e-01 0.00e+00 1.19e-04 -7.7 7.96e-02 -3.0 1.00e+00 9.45e-01f 1
224 2.8117611e-01 0.00e+00 1.40e-04 -6.9 4.77e-01 -3.4 1.00e+00 2.96e-01f 1
225 2.8033847e-01 0.00e+00 1.04e-04 -7.6 8.59e-02 -3.0 1.00e+00 7.96e-01f 1
226 2.8005033e-01 0.00e+00 9.73e-05 -9.1 3.26e-02 -2.6 1.00e+00 6.19e-01f 1
Number of Iterations....: 226
(scaled) (unscaled)
Objective...............: 2.8005032523583379e-01 2.8005032523583379e-01
Dual infeasibility......: 9.7272674831558608e-05 9.7272674831558608e-05
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 3.2315149852880829e-07 3.2315149852880829e-07
Overall NLP error.......: 9.7272674831558608e-05 9.7272674831558608e-05
Number of objective function evaluations = 227
Number of objective gradient evaluations = 227
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 228
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 1
Number of Lagrangian Hessian evaluations = 226
Total CPU secs in IPOPT (w/o function evaluations) = 3403.326
Total CPU secs in NLP function evaluations = 214.977
EXIT: Optimal Solution Found.
....在此分辨率下，定时是可以的，但在较高分辨率下，线性求解变得非常大且非常慢。所以我想我的问题是：我可以期望这样的事情（在高分辨率下，具有约500 000个参数）需要几天的时间来解决吗，或者是否有任何我可以调整的设置来提高收敛性或减少迭代次数需要。实际上，最初的猜测是相当不错的，而实际上，我要寻找的是局部最优。
答案 0 :(得分：1)
看来您的方法非常周到。约有500k变量和100k约束，您拥有很大的自由度。内点法（其中IPOPT相当不错）的主要替代方法是主动集法。主动集方法通常在很少的自由度下会更好，因此IPOPT是您最好的选择。
IPOPT输出表明以下几点：
Hessian不是正定的（几乎每个迭代都需要正则化）
正则化之后，问题在可变范围内足够凸（无回溯线搜索）
IPOPT时间为>>函数调用时间（3403.326：214.977非常大）。大部分时间是在矩阵分解中。
由于变量范围的限制，几乎每次迭代都被截断。
据我了解，当您的问题太大时，它将超出硬件限制（CPU缓存），并且线性代数时间会变长。这可能是您的主要问题。
由于这些原因，我建议尝试使用BFGS方法（IPOPT option）。通过直接计算Hessian的近似逆，可以避免困难的矩阵分解/求解。此外，BFGS方法可以保证正定的Hessian。通常，当无法使用Hessian时使用BFGS近似值，因为确切的Hessian应该提供更准确的步长。但是有了您的正则化，昂贵的因式分解和截断的步骤，BFGS可能会变得差不多。期望有更多的迭代（226很小），但是每次迭代都应该快得多。
您可能还想放宽变量范围。内点方法旨在避免越界。有这么多界限，可能会减慢进度。
答案 1 :(得分：0)
不是一个肯定的答案，但是评论太久了：Ipopt应该已经进行了优化，因此，除非您更改整个算法，否则恐怕您不会得到更好的结果。
如果您正在寻找局部最优值，则从粗略的分辨率开始，然后选择“最有希望的”部分（即，最有可能找到最优值的部分）。然后在该部分上提高分辨率 ，然后从二分法开始。
您还可以检查神经网络，它可以对复杂的非线性函数进行建模，并且现在已经成熟，可以利用CPU + GPU架构的大量实现来提供很多帮助。渐变backprop旨在有效地找到局部极值。