basin 0.6.0

An optimization library for Rust
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

//! Integration tests for the log-barrier [`BarrierMethod`] on linearly
//! constrained quadratics over the plain `Vec<f64>` backend, using the
//! hand-rolled [`DenseMatrix`]. Mirrors `barrier_method_nalgebra.rs`; proves
//! the constraint solver now runs on the default backend with no external
//! linear-algebra crate.

use basin::problems::ConstrainedQuadratic;
use basin::{
    Backtracking, BarrierMethod, BasicState, DenseMatrix, Executor, GradientDescent, GradientState,
    TerminationReason,
};

/// `min ‖x − (2,2)‖²` s.t. `x₀ + x₁ ≤ 2`. The unconstrained min (2,2) is
/// infeasible; the constrained optimum is the projection (1,1).
fn active_problem() -> ConstrainedQuadratic<DenseMatrix, Vec<f64>> {
    ConstrainedQuadratic::new(
        vec![2.0, 2.0],
        DenseMatrix::from_row_slice(1, 2, &[1.0, 1.0]),
        vec![2.0],
    )
}

#[test]
fn active_constraint_converges_to_projection() {
    let problem = active_problem();
    let initial = vec![0.0, 0.0]; // strictly feasible (sum 0 < 2)

    let result = Executor::new(
        problem,
        BarrierMethod::new(GradientDescent::with_line_search(Backtracking::new())),
        BasicState::new(initial),
    )
    .max_iter(50)
    .run();

    assert_eq!(result.reason, TerminationReason::SolverConverged);
    assert!(
        (result.param()[0] - 1.0).abs() < 1e-4 && (result.param()[1] - 1.0).abs() < 1e-4,
        "expected (1, 1), got {:?}",
        result.param()
    );
}

#[test]
fn inactive_constraint_recovers_unconstrained_minimum() {
    // Center inside the feasible region: unconstrained min (0.5, 0.5),
    // sum 1.0 < 2, so the constraint is slack at the optimum.
    let problem = ConstrainedQuadratic::new(
        vec![0.5, 0.5],
        DenseMatrix::from_row_slice(1, 2, &[1.0, 1.0]),
        vec![2.0],
    );
    let initial = vec![0.0, 0.0];

    let result = Executor::new(
        problem,
        BarrierMethod::new(GradientDescent::with_line_search(Backtracking::new())),
        BasicState::new(initial),
    )
    .max_iter(50)
    .run();

    assert_eq!(result.reason, TerminationReason::SolverConverged);
    assert!(
        (result.param()[0] - 0.5).abs() < 1e-4 && (result.param()[1] - 0.5).abs() < 1e-4,
        "expected (0.5, 0.5), got {:?}",
        result.param()
    );
}

#[test]
fn infeasible_start_is_reported_as_failure() {
    let problem = active_problem();
    // sum 4.0 > 2 ⇒ A x₀ ≰ b ⇒ infeasible.
    let initial = vec![2.0, 2.0];

    let result = Executor::new(
        problem,
        BarrierMethod::new(GradientDescent::with_line_search(Backtracking::new())),
        BasicState::new(initial),
    )
    .max_iter(50)
    .run();

    assert_eq!(result.reason, TerminationReason::SolverFailed);
}

#[test]
fn eval_counts_are_recorded() {
    let problem = active_problem();
    let initial = vec![0.0, 0.0];

    let result = Executor::new(
        problem,
        BarrierMethod::new(GradientDescent::with_line_search(Backtracking::new())),
        BasicState::new(initial),
    )
    .max_iter(50)
    .run();

    // Inner barrier solves plus the per-outer-iter true-objective evals must
    // have accumulated onto the outer state.
    assert!(result.cost_evals() > 0, "no cost evals recorded");
    assert!(
        result.state.gradient_evals() > 0,
        "no gradient evals recorded"
    );
}

/// Two active constraints exercise the multi-row `Aᵀ·(μ/s)` sum in the
/// barrier gradient — and the `DenseMatrix` transpose-matvec on a `2×2`. `min
/// ‖x − (2,2)‖²` s.t. `x₀ + x₁ ≤ 2` and `x₀ ≤ 0.5` has both constraints active
/// at the optimum `(0.5, 1.5)`.
#[test]
fn two_constraints_both_active() {
    let problem = ConstrainedQuadratic::new(
        vec![2.0, 2.0],
        DenseMatrix::from_row_slice(2, 2, &[1.0, 1.0, 1.0, 0.0]),
        vec![2.0, 0.5],
    );
    let initial = vec![0.0, 0.0]; // 0<2 and 0<0.5: strictly feasible

    let result = Executor::new(
        problem,
        BarrierMethod::new(GradientDescent::with_line_search(Backtracking::new())),
        BasicState::new(initial),
    )
    .max_iter(50)
    .run();

    assert_eq!(result.reason, TerminationReason::SolverConverged);
    assert!(
        (result.param()[0] - 0.5).abs() < 1e-4 && (result.param()[1] - 1.5).abs() < 1e-4,
        "expected (0.5, 1.5), got {:?}",
        result.param()
    );
}