newton_example/
newton_example.rs

1use nalgebra::{DMatrix, DVector};
2use optimization_solvers::{FuncEvalMultivariate, LineSearchSolver, MoreThuente, Newton, Tracer};
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 function: f(x,y) = x^2 + y^2 + exp(x^2 + y^2)
10    // This function is convex and has a unique minimum at (0, 0)
11    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
12        let x1 = x[0];
13        let x2 = x[1];
14
15        // Function value
16        let f = x1.powi(2) + x2.powi(2) + (x1.powi(2) + x2.powi(2)).exp();
17
18        // Gradient: ∇f = [2x + 2x*exp(x^2+y^2), 2y + 2y*exp(x^2+y^2)]
19        let exp_term = (x1.powi(2) + x2.powi(2)).exp();
20        let g1 = 2.0 * x1 * (1.0 + exp_term);
21        let g2 = 2.0 * x2 * (1.0 + exp_term);
22        let g = DVector::from_vec(vec![g1, g2]);
23
24        // Hessian: ∇²f = [[2(1+exp) + 4x^2*exp, 4xy*exp], [4xy*exp, 2(1+exp) + 4y^2*exp]]
25        let h11 = 2.0 * (1.0 + exp_term) + 4.0 * x1.powi(2) * exp_term;
26        let h12 = 4.0 * x1 * x2 * exp_term;
27        let h21 = h12;
28        let h22 = 2.0 * (1.0 + exp_term) + 4.0 * x2.powi(2) * exp_term;
29        let hessian = DMatrix::from_vec(2, 2, vec![h11, h21, h12, h22]);
30
31        FuncEvalMultivariate::new(f, g).with_hessian(hessian)
32    };
33
34    // Setting up the line search (More-Thuente line search)
35    let mut ls = MoreThuente::default();
36
37    // Setting up the solver
38    let tol = 1e-6;
39    let x0 = DVector::from_vec(vec![1.0, 1.0]); // Starting point
40    let mut solver = Newton::new(tol, x0.clone());
41
42    // Running the solver
43    let max_iter_solver = 20;
44    let max_iter_line_search = 20;
45
46    println!("=== Newton's Method Example ===");
47    println!("Objective: f(x,y) = x^2 + y^2 + exp(x^2 + y^2) (convex)");
48    println!("Global minimum: (0, 0) with f(0,0) = 1");
49    println!("Starting point: {:?}", x0);
50    println!("Tolerance: {}", tol);
51    println!();
52
53    match solver.minimize(
54        &mut ls,
55        f_and_g,
56        max_iter_solver,
57        max_iter_line_search,
58        None,
59    ) {
60        Ok(()) => {
61            let x = solver.x();
62            let eval = f_and_g(x);
63            println!("✅ Optimization completed successfully!");
64            println!("Final iterate: {:?}", x);
65            println!("Function value: {:.6}", eval.f());
66            println!("Gradient norm: {:.6}", eval.g().norm());
67            println!("Iterations: {}", solver.k());
68
69            // Show Newton decrement
70            if let Some(decrement_squared) = solver.decrement_squared() {
71                println!("Newton decrement squared: {:.6}", decrement_squared);
72                println!("Newton decrement: {:.6}", decrement_squared.sqrt());
73            }
74
75            // Check if we're close to the known minimum
76            let true_min = DVector::from_vec(vec![0.0, 0.0]);
77            let distance_to_min = (x - true_min).norm();
78            println!("Distance to true minimum: {:.6}", distance_to_min);
79            println!("Expected function value: 1.0");
80        }
81        Err(e) => {
82            println!("❌ Optimization failed: {:?}", e);
83        }
84    }
85}
newton_example/newton_example.rs

newton_example/
newton_example.rs
