| 
59 | 59 |     "Formally, the goal of BADS is to *minimize* a target (or objective) function $f(\\mathbf{x}): \\mathbb{R}^D \\rightarrow \\mathbb{R}$, for $\\mathbf{x} \\in \\mathbb{R}^D$,\n",  | 
60 | 60 |     "\n",  | 
61 | 61 |     "$$\n",  | 
62 |  | -    "\\mathbf{x}^\\star = \\arg\\min_\\mathbf{x} f(\\mathbf{x}) \\qquad \\text{with} \\; \\text{lower_bounds}_d \\le x_d \\le \\text{upper_bounds}_d \\; \\text{ for } 1\\le d \\le D,\n",  | 
 | 62 | +    "\\mathbf{x}^\\star = \\arg\\min_\\mathbf{x} f(\\mathbf{x}) \\qquad \\text{with} \\quad \\text{lower\\_bounds}_d \\le x_d \\le \\text{upper\\_bounds}_d \\; \\text{ for } 1\\le d \\le D,\n",  | 
63 | 63 |     "$$\n",  | 
64 | 64 |     "where $D$ is the dimensionality of the problem and `lower_bounds`, `upper_bounds` are arrays representing lower/upper bound constraints, which can be set to infinite for unbounded parameters."  | 
65 | 65 |    ]  | 
 | 
131 | 131 |       "     0           6               1               1         Initial mesh            Initial points\n",  | 
132 | 132 |       "     0          10               1             0.5         Refine grid             Train\n",  | 
133 | 133 |       "     1          18               1            0.25         Refine grid             Train\n",  | 
134 |  | -      "     2          22        0.250428            0.25     Successful search (ES-wcm)        \n",  | 
135 |  | -      "     2          24       0.0851394            0.25     Successful search (ES-ell)        \n",  | 
136 |  | -      "     2          26      0.00997961            0.25     Incremental search (ES-ell)        \n",  | 
137 |  | -      "     2          27     0.000224117            0.25     Incremental search (ES-ell)        \n",  | 
138 |  | -      "     2          34     0.000224117           0.125         Refine grid             \n",  | 
139 |  | -      "     3          42     0.000224117          0.0625         Refine grid             Train\n",  | 
140 |  | -      "     4          44     7.97867e-05          0.0625     Incremental search (ES-wcm)        \n",  | 
141 |  | -      "     4          50     7.97867e-05         0.03125         Refine grid             \n",  | 
142 |  | -      "     5          58     7.97867e-05       0.0078125         Refine grid             \n",  | 
143 |  | -      "     6          66     7.97867e-05      0.00195312         Refine grid             Train\n",  | 
 | 134 | +      "     2          20        0.608156            0.25     Successful search (ES-ell)        \n",  | 
 | 135 | +      "     2          21        0.408646            0.25     Successful search (ES-ell)        \n",  | 
 | 136 | +      "     2          23        0.303906            0.25     Incremental search (ES-wcm)        \n",  | 
 | 137 | +      "     2          25        0.212582            0.25     Incremental search (ES-ell)        \n",  | 
 | 138 | +      "     2          30        0.212582           0.125         Refine grid             Train\n",  | 
 | 139 | +      "     3          32        0.127714           0.125     Successful search (ES-wcm)        \n",  | 
 | 140 | +      "     3          33       0.0139198           0.125     Successful search (ES-wcm)        \n",  | 
 | 141 | +      "     3          34     0.000681342           0.125     Incremental search (ES-wcm)        \n",  | 
 | 142 | +      "     3          42     0.000681342          0.0625         Refine grid             Train\n",  | 
 | 143 | +      "     4          44     0.000120297          0.0625     Incremental search (ES-ell)        \n",  | 
 | 144 | +      "     4          50     0.000120297         0.03125         Refine grid             Train\n",  | 
 | 145 | +      "     5          58     0.000120297        0.015625         Refine grid             Train\n",  | 
 | 146 | +      "     6          66     0.000120297      0.00390625         Refine grid             Train\n",  | 
 | 147 | +      "     7          69     2.70979e-05      0.00390625     Incremental search (ES-wcm)        \n",  | 
 | 148 | +      "     7          74     2.70979e-05     0.000976562         Refine grid             Train\n",  | 
144 | 149 |       "Optimization terminated: change in the function value less than options['tol_fun'].\n",  | 
145 |  | -      "Function value at minimum: 7.97867122044391e-05\n",  | 
 | 150 | +      "Function value at minimum: 2.7097907605695835e-05\n",  | 
146 | 151 |       "\n"  | 
147 | 152 |      ]  | 
148 | 153 |     }  | 
 | 
173 | 178 |      "name": "stdout",  | 
174 | 179 |      "output_type": "stream",  | 
175 | 180 |      "text": [  | 
176 |  | -      "BADS minimum at: x_min = [1.00744247 1.01543427], fval = 7.979e-05\n",  | 
177 |  | -      "total f-count: 67, time: 1.34 s\n"  | 
 | 181 | +      "BADS minimum at: x_min = [0.99709786 0.993772  ], fval = 2.71e-05\n",  | 
 | 182 | +      "total f-count: 75, time: 1.13 s\n"  | 
178 | 183 |      ]  | 
179 | 184 |     }  | 
180 | 185 |    ],  | 
 | 
216 | 221 |    "name": "python",  | 
217 | 222 |    "nbconvert_exporter": "python",  | 
218 | 223 |    "pygments_lexer": "ipython3",  | 
219 |  | -   "version": "3.9.16"  | 
 | 224 | +   "version": "3.13.1"  | 
220 | 225 |   },  | 
221 | 226 |   "vscode": {  | 
222 | 227 |    "interpreter": {  | 
 | 
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