gradient_descent_example/
gradient_descent_example.rs

1use nalgebra::DVector;
2use optimization_solvers::{
3    BackTracking, FuncEvalMultivariate, GradientDescent, LineSearchSolver, Tracer,
4};
5
6fn main() {
7    // Setting up logging
8    std::env::set_var("RUST_LOG", "info");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10
11    // Convex quadratic function: f(x,y) = x^2 + 2y^2
12    // Global minimum at (0, 0) with f(0,0) = 0
13    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
14        let x1 = x[0];
15        let x2 = x[1];
16
17        // Function value
18        let f = x1.powi(2) + 2.0 * x2.powi(2);
19
20        // Gradient
21        let g1 = 2.0 * x1;
22        let g2 = 4.0 * x2;
23        let g = DVector::from_vec(vec![g1, g2]);
24
25        FuncEvalMultivariate::new(f, g)
26    };
27
28    // Setting up the line search (backtracking with Armijo condition)
29    let armijo_factor = 1e-4;
30    let beta = 0.5;
31    let mut ls = BackTracking::new(armijo_factor, beta);
32
33    // Setting up the solver
34    let tol = 1e-6;
35    let x0 = DVector::from_vec(vec![2.0, 1.0]); // Starting point
36    let mut solver = GradientDescent::new(tol, x0.clone());
37
38    // Running the solver
39    let max_iter_solver = 100;
40    let max_iter_line_search = 20;
41
42    println!("=== Gradient Descent Example ===");
43    println!("Objective: f(x,y) = x^2 + 2y^2 (convex quadratic)");
44    println!("Global minimum: (0, 0) with f(0,0) = 0");
45    println!("Starting point: {:?}", x0);
46    println!("Tolerance: {}", tol);
47    println!();
48
49    match solver.minimize(
50        &mut ls,
51        f_and_g,
52        max_iter_solver,
53        max_iter_line_search,
54        None,
55    ) {
56        Ok(()) => {
57            let x = solver.x();
58            let eval = f_and_g(x);
59            println!("✅ Optimization completed successfully!");
60            println!("Final iterate: {:?}", x);
61            println!("Function value: {:.6}", eval.f());
62            println!("Gradient norm: {:.6}", eval.g().norm());
63            println!("Iterations: {}", solver.k());
64
65            // Check if we're close to the known minimum
66            let true_min = DVector::from_vec(vec![0.0, 0.0]);
67            let distance_to_min = (x - true_min).norm();
68            println!("Distance to true minimum: {:.6}", distance_to_min);
69            println!("Expected function value: 0.0");
70        }
71        Err(e) => {
72            println!("❌ Optimization failed: {:?}", e);
73        }
74    }
75}
gradient_descent_example/gradient_descent_example.rs

gradient_descent_example/
gradient_descent_example.rs
