bfgs_example/
bfgs_example.rs

1use nalgebra::DVector;
2use optimization_solvers::{FuncEvalMultivariate, LineSearchSolver, MoreThuente, Tracer, BFGS};
3
4fn main() {
5    // Setting up logging
6    std::env::set_var("RUST_LOG", "info");
7    let _ = Tracer::default().with_normal_stdout_layer().build();
8
9    // Convex quadratic function: f(x,y,z) = x^2 + 2y^2 + 3z^2 + xy + yz
10    // This function has a unique minimum that we can verify
11    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
12        let x1 = x[0];
13        let x2 = x[1];
14        let x3 = x[2];
15
16        // Function value
17        let f = x1.powi(2) + 2.0 * x2.powi(2) + 3.0 * x3.powi(2) + x1 * x2 + x2 * x3;
18
19        // Gradient
20        let g1 = 2.0 * x1 + x2;
21        let g2 = 4.0 * x2 + x1 + x3;
22        let g3 = 6.0 * x3 + x2;
23        let g = DVector::from_vec(vec![g1, g2, g3]);
24
25        FuncEvalMultivariate::new(f, g)
26    };
27
28    // Setting up the line search (More-Thuente line search)
29    let mut ls = MoreThuente::default();
30
31    // Setting up the solver
32    let tol = 1e-8;
33    let x0 = DVector::from_vec(vec![1.0, 1.0, 1.0]); // Starting point
34    let mut solver = BFGS::new(tol, x0.clone());
35
36    // Running the solver
37    let max_iter_solver = 50;
38    let max_iter_line_search = 20;
39
40    println!("=== BFGS Quasi-Newton Example ===");
41    println!("Objective: f(x,y,z) = x^2 + 2y^2 + 3z^2 + xy + yz (convex quadratic)");
42    println!("Starting point: {:?}", x0);
43    println!("Tolerance: {}", tol);
44    println!();
45
46    match solver.minimize(
47        &mut ls,
48        f_and_g,
49        max_iter_solver,
50        max_iter_line_search,
51        None,
52    ) {
53        Ok(()) => {
54            let x = solver.x();
55            let eval = f_and_g(x);
56            println!("✅ Optimization completed successfully!");
57            println!("Final iterate: {:?}", x);
58            println!("Function value: {:.8}", eval.f());
59            println!("Gradient norm: {:.8}", eval.g().norm());
60            println!("Iterations: {}", solver.k());
61
62            // Verify optimality conditions
63            let gradient_at_solution = eval.g();
64            println!("Gradient at solution: {:?}", gradient_at_solution);
65            println!(
66                "Gradient norm should be close to 0: {}",
67                gradient_at_solution.norm()
68            );
69
70            // For this convex quadratic function, the minimum should be at the solution of the linear system
71            // ∇f(x) = 0, which gives us a system of linear equations
72            println!("Expected minimum: solution of ∇f(x) = 0");
73        }
74        Err(e) => {
75            println!("❌ Optimization failed: {:?}", e);
76        }
77    }
78}
bfgs_example/bfgs_example.rs

bfgs_example/
bfgs_example.rs
