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Expand file tree Collapse file tree Original file line number Diff line number Diff line change 1111export variational
1212
1313function variational (; n:: Int = default_nvar, kwargs... )
14- h = 1 // (n + 1 )
15- x0 = [(i * h) * (1 - i * h) for i = 1 : n]
16- model = Model ()
17- @variable (model, x[i = 1 : n], start = x0[i])
14+ h = 1 // (n + 1 )
15+ x0 = [(i * h) * (1 - i * h) for i ∈ 1 : n]
16+ model = Model ()
17+ @variable (model, x[i= 1 : n], start = x0[i])
1818
19- @objective (
20- model,
21- Min,
22- 2 * (
23- (sum (x[i] * (x[i] - x[i + 1 ]) / h for i = 1 : (n - 1 )) + x[n] * x[n] / h) +
24- n *
25- (h / 2 ) *
26- (
27- (exp (x[1 ]) - exp (0 )) / (x[1 ] - 0 ) +
28- sum ((exp (x[j + 1 ]) - exp (x[j])) / (x[j + 1 ] - x[j]) for j = 1 : (n - 1 )) +
29- (exp (0 ) - exp (x[n])) / (0 - x[n])
30- )
31- )
32- )
19+ @objective (
20+ model,
21+ Min,
22+ 2 * (
23+ (sum (x[i] * (x[i] - x[i+ 1 ]) / h for i ∈ 1 : (n- 1 )) + x[n] * x[n] / h) +
24+ n *
25+ (h / 2 ) *
26+ (
27+ (exp (x[1 ]) - exp (0 )) / (x[1 ] - 0 ) +
28+ sum ((exp (x[j+ 1 ]) - exp (x[j])) / (x[j+ 1 ] - x[j]) for j ∈ 1 : (n- 1 )) +
29+ (exp (0 ) - exp (x[n])) / (0 - x[n])
30+ )
31+ )
32+ )
3333
34- return model
34+ return model
3535end
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