oximo 0.5.0

A Rust algebraic modeling library for solving optimization problems
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231

//! Integration tests for the POUNCE backend through the umbrella crate.
//! POUNCE runs on stable Rust (finite differences), so these need only
//! `--features pounce`. `--features pounce-enzyme` solves the same models with
//! exact derivatives.

#![cfg(feature = "pounce")]

use oximo::pounce::{MuStrategy, PounceOptions};
use oximo::prelude::*;
use oximo::solvers::Pounce;

fn assert_close(got: f64, want: f64, tol: f64, what: &str) {
    assert!((got - want).abs() < tol, "{what}: got {got}, want {want}");
}

/// Relative closeness for two independent interior-point solves.
fn close(a: f64, b: f64) -> bool {
    (a - b).abs() <= 1e-5 * a.abs().max(b.abs()).max(1.0)
}

/// Hock-Schittkowski 071:
/// min x1 x4 (x1 + x2 + x3) + x3 s.t. x1 x2 x3 x4 >= 25,
/// x1^2 + x2^2 + x3^2 + x4^2 == 40, 1 <= x <= 5.
/// Optimum approx 17.014 at (1.0, 4.743, 3.82115, 1.37941).
#[test]
fn hs071() {
    let m = Model::new("hs071");
    variable!(m, 1.0 <= x1 <= 5.0, initial = 1.0);
    variable!(m, 1.0 <= x2 <= 5.0, initial = 5.0);
    variable!(m, 1.0 <= x3 <= 5.0, initial = 5.0);
    variable!(m, 1.0 <= x4 <= 5.0, initial = 1.0);
    objective!(m, Min, x1 * x4 * (x1 + x2 + x3) + x3);
    constraint!(m, prod, x1 * x2 * x3 * x4 >= 25.0);
    constraint!(m, ssq, x1.powi(2) + x2.powi(2) + x3.powi(2) + x4.powi(2) == 40.0);

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(res.has_solution(), "hs071 should solve");
    assert_close(res.value_of(x1).unwrap(), 1.0, 1e-3, "x1");
    assert_close(res.value_of(x2).unwrap(), 4.743, 1e-3, "x2");
    assert_close(res.value_of(x4).unwrap(), 1.379_408, 1e-3, "x4");
    assert_close(res.objective().unwrap(), 17.014, 1e-2, "objective");
}

#[test]
fn rosenbrock_unconstrained() {
    let m = Model::new("rosenbrock");
    variable!(m, -10.0 <= x <= 10.0, initial = -1.2);
    variable!(m, -10.0 <= y <= 10.0, initial = 1.0);
    objective!(m, Min, (1.0 - x).powi(2) + 100.0 * (y - x.powi(2)).powi(2));

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert_eq!(res.termination, TerminationStatus::LocallyOptimal);
    assert_close(res.value_of(x).unwrap(), 1.0, 1e-4, "x");
    assert_close(res.value_of(y).unwrap(), 1.0, 1e-4, "y");
    assert!(res.objective().unwrap().abs() < 1e-6, "objective");
}

#[test]
fn maximize_flips_sign_back() {
    // max 4x - x^2 -> x = 2, objective 4.
    let m = Model::new("max");
    variable!(m, -10.0 <= x <= 10.0);
    objective!(m, Max, 4.0 * x - x.powi(2));

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert_eq!(res.termination, TerminationStatus::LocallyOptimal);
    assert_close(res.value_of(x).unwrap(), 2.0, 1e-4, "x");
    assert_close(res.objective().unwrap(), 4.0, 1e-5, "objective");
}

#[test]
fn quadratic_constraint_qcp() {
    // min x + y s.t. x^2 + y^2 <= 1 -> x = y = -1/sqrt(2).
    let m = Model::new("qcp");
    variable!(m, -2.0 <= x <= 2.0);
    variable!(m, -2.0 <= y <= 2.0);
    constraint!(m, ball, x.powi(2) + y.powi(2) <= 1.0);
    objective!(m, Min, x + y);

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(res.has_solution());
    let r = -1.0 / 2.0_f64.sqrt();
    assert_close(res.value_of(x).unwrap(), r, 1e-4, "x");
    assert_close(res.value_of(y).unwrap(), r, 1e-4, "y");
}

#[test]
fn lp_duals_match_lp_convention() {
    let m = Model::new("product_mix");
    variable!(m, x >= 0.0);
    variable!(m, y >= 0.0);
    variable!(m, z >= 0.0);
    let labor = constraint!(m, labor, x + y + z <= 12.0);
    let material = constraint!(m, material, 2.0 * x + y + 3.0 * z <= 16.0);
    objective!(m, Max, 40.0 * x + 30.0 * y + 20.0 * z);

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(res.has_solution());
    assert_close(res.objective().unwrap(), 400.0, 1e-3, "objective");
    assert_close(res.value_of(x).unwrap(), 4.0, 1e-3, "x");
    assert_close(res.value_of(y).unwrap(), 8.0, 1e-3, "y");
    assert_close(res.dual_of(labor).unwrap(), 20.0, 1e-3, "labor dual");
    assert_close(res.dual_of(material).unwrap(), 10.0, 1e-3, "material dual");

    let z_id = m.variable_id("z").unwrap();
    assert_close(res.reduced_costs[&z_id], -30.0, 1e-3, "z reduced cost");
    assert!(res.iterations > 0, "iteration count should be reported");
}

#[test]
fn indexed_least_squares_qp() {
    // min sum_i (x_i - t_i)^2 s.t. sum_i x_i == 8 with t = [1, 2, 3, 4].
    // The projection shifts every x_i by (8 - 10) / 4: x_i = t_i - 0.5,
    // objective 4 * 0.25 = 1.
    let t = [1.0, 2.0, 3.0, 4.0];
    let n = t.len();

    let m = Model::new("least_squares");
    variable!(m, 0.0 <= x[i in 0..n] <= 10.0);
    constraint!(m, total, sum!(x[i] for i in 0..n) == 8.0);
    objective!(m, Min, sum!((x[i] - t[i]).powi(2) for i in 0..n));

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(res.has_solution());
    assert_close(res.objective().unwrap(), 1.0, 1e-4, "objective");
    for i in 0..n {
        assert_close(res.value_of(x[i]).unwrap(), t[i] - 0.5, 1e-4, &format!("x[{i}]"));
    }
}

#[test]
fn feasibility_problem_returns_feasible_point() {
    let m = Model::new("feas");
    variable!(m, -2.0 <= x <= 2.0);
    variable!(m, -2.0 <= y <= 2.0);
    constraint!(m, disk, x.powi(2) + y.powi(2) <= 1.0);
    constraint!(m, line, x + y >= 1.0);
    objective!(m, Feasibility);

    let res = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(res.has_solution(), "feasibility solve should return a point");
    let (xv, yv) = (res.value_of(x).unwrap(), res.value_of(y).unwrap());
    assert!(xv * xv + yv * yv <= 1.0 + 1e-5, "inside disk: ({xv}, {yv})");
    assert!(xv + yv >= 1.0 - 1e-5, "above line: ({xv}, {yv})");
}

#[test]
fn integer_models_are_rejected() {
    let m = Model::new("milp");
    variable!(m, 0.0 <= x <= 5.0, Int);
    objective!(m, Min, x);

    let err = Pounce.solve(&m, &PounceOptions::default()).unwrap_err();
    assert!(matches!(err, SolverError::UnsupportedKind(ModelKind::MILP)));
}

#[test]
fn persistent_matches_cold_on_parameter_sweep() {
    let m = Model::new("nlp_sweep");
    param!(m, w = 1.0);
    variable!(m, 0.1 <= x <= 10.0, initial = 1.0);
    variable!(m, 0.1 <= y <= 10.0, initial = 1.0);
    constraint!(m, prod, x * y >= 4.0);
    objective!(m, Min, w * x + y);

    let mut solver = Pounce.persistent();
    for wv in [1.0, 2.0, 0.5] {
        w.set_param_value(wv);
        let warm = solver.solve(&m, &PounceOptions::default()).unwrap();
        let cold = Pounce.solve(&m, &PounceOptions::default()).unwrap();
        assert!(warm.has_solution(), "w {wv}: no solution");
        assert!(close(warm.objective().unwrap(), cold.objective().unwrap()), "w {wv}: objective");
        assert!(close(warm.value_of(x).unwrap(), cold.value_of(x).unwrap()), "w {wv}: x");
        assert!(close(warm.value_of(y).unwrap(), cold.value_of(y).unwrap()), "w {wv}: y");
    }
}

#[test]
fn typed_options_still_solve() {
    let m = Model::new("hs071_opts");
    variable!(m, 1.0 <= x1 <= 5.0, initial = 1.0);
    variable!(m, 1.0 <= x2 <= 5.0, initial = 5.0);
    variable!(m, 1.0 <= x3 <= 5.0, initial = 5.0);
    variable!(m, 1.0 <= x4 <= 5.0, initial = 1.0);
    objective!(m, Min, x1 * x4 * (x1 + x2 + x3) + x3);
    constraint!(m, prod, x1 * x2 * x3 * x4 >= 25.0);
    constraint!(m, ssq, x1.powi(2) + x2.powi(2) + x3.powi(2) + x4.powi(2) == 40.0);

    let opts = PounceOptions::default()
        .tol(1e-8)
        .max_iter(500)
        .mu_strategy(MuStrategy::Adaptive)
        .mu_oracle("probing")
        .presolve(false);

    let res = Pounce.solve(&m, &opts).unwrap();
    assert!(res.has_solution(), "hs071 should solve with typed options");
    assert_close(res.objective().unwrap(), 17.014, 1e-2, "objective");
}

#[test]
fn unknown_option_is_rejected() {
    let m = Model::new("reject");
    variable!(m, 0.0 <= x <= 5.0, initial = 1.0);
    objective!(m, Min, (x - 2.0).powi(2));

    let opts = PounceOptions::default().set("not_a_real_option", 1);
    let err = Pounce.solve(&m, &opts).unwrap_err();
    assert!(matches!(err, SolverError::Backend(_)), "cold: got {err:?}");

    let mut solver = Pounce.persistent();
    let err = solver.solve(&m, &opts).unwrap_err();
    assert!(matches!(err, SolverError::Backend(_)), "persistent: got {err:?}");
}

#[test]
fn verbose_captures_raw_log() {
    let m = Model::new("logged");
    variable!(m, -10.0 <= x <= 10.0, initial = -1.2);
    objective!(m, Min, (x - 2.0).powi(2));

    let quiet = Pounce.solve(&m, &PounceOptions::default()).unwrap();
    assert!(quiet.raw_log.is_none(), "no log capture without verbose");

    let mut opts = PounceOptions::default();
    opts.universal.verbose = Some(true);
    let res = Pounce.solve(&m, &opts).unwrap();
    assert!(res.iterations > 0, "solve reports iterations");
    let log = res.raw_log.expect("verbose solve should capture a log");
    assert!(log.contains("EXIT:"), "log has the exit status: {log}");
}