optimization_solvers::steepest_descent::gradient_descent

Struct GradientDescent

pub struct GradientDescent {
    pub grad_tol: Floating,
    pub x: DVector<Floating>,
    pub k: usize,
}

Fields§

§grad_tol: Floating§x: DVector<Floating>§k: usize

Implementations§

Source §

impl GradientDescent

Auto-generated by derive_getters::Getters.

Source

pub fn grad_tol(&self) -> &Floating

Get field grad_tol from instance of GradientDescent.

Source

pub fn x(&self) -> &DVector<Floating>

Get field x from instance of GradientDescent.

Examples found in repository ?

examples/quadratic_with_plots.rs (line 28)

6fn main() {
7    // Setting up log verbosity and _.
8    std::env::set_var("RUST_LOG", "debug");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10    // Setting up the oracle
11    let matrix = DMatrix::from_vec(2, 2, vec![100., 0., 0., 100.]);
12    let mut f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
13        let f = x.dot(&(&matrix * x));
14        let g = 2. * &matrix * x;
15        FuncEvalMultivariate::new(f, g)
16    };
17    // Setting up the line search
18    let armijo_factr = 1e-4;
19    let beta = 0.5; // (beta in (0, 1), ntice that beta = 0.5 corresponds to bisection)
20    let mut ls = BackTracking::new(armijo_factr, beta);
21    // Setting up the main solver, with its parameters and the initial guess
22    let tol = 1e-6;
23    let x0 = DVector::from_vec(vec![10., 10.]);
24    let mut solver = GradientDescent::new(tol, x0);
25    // We define a callback to store iterates and function evaluations
26    let mut iterates = vec![];
27    let mut solver_callback = |s: &GradientDescent| {
28        iterates.push(s.x().clone());
29    };
30    // Running the solver
31    let max_iter_solver = 100;
32    let max_iter_line_search = 10;
33
34    solver
35        .minimize(
36            &mut ls,
37            f_and_g,
38            max_iter_solver,
39            max_iter_line_search,
40            Some(&mut solver_callback),
41        )
42        .unwrap();
43    // Printing the result
44    let x = solver.x();
45    let eval = f_and_g(x);
46    println!("x: {:?}", x);
47    println!("f(x): {}", eval.f());
48    println!("g(x): {:?}", eval.g());
49
50    // Plotting the iterates
51    let n = 50;
52    let start = -5.0;
53    let end = 5.0;
54    let plotter = Plotter3d::new(start, end, start, end, n)
55        .append_plot(&mut f_and_g, "Objective function", 0.5)
56        .append_scatter_points(&mut f_and_g, &iterates, "Iterates")
57        .set_layout_size(1600, 1000);
58    plotter.build("quadratic.html");
59}

More examples

Hide additional examples

examples/gradient_descent_example.rs (line 57)

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}

Source

pub fn k(&self) -> &usize

Get field k from instance of GradientDescent.

Examples found in repository ?

examples/gradient_descent_example.rs (line 63)

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}

Source §

impl GradientDescent

Source

pub fn new(grad_tol: Floating, x0: DVector<Floating>) -> Self

Examples found in repository ?

examples/quadratic_with_plots.rs (line 24)

6fn main() {
7    // Setting up log verbosity and _.
8    std::env::set_var("RUST_LOG", "debug");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10    // Setting up the oracle
11    let matrix = DMatrix::from_vec(2, 2, vec![100., 0., 0., 100.]);
12    let mut f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
13        let f = x.dot(&(&matrix * x));
14        let g = 2. * &matrix * x;
15        FuncEvalMultivariate::new(f, g)
16    };
17    // Setting up the line search
18    let armijo_factr = 1e-4;
19    let beta = 0.5; // (beta in (0, 1), ntice that beta = 0.5 corresponds to bisection)
20    let mut ls = BackTracking::new(armijo_factr, beta);
21    // Setting up the main solver, with its parameters and the initial guess
22    let tol = 1e-6;
23    let x0 = DVector::from_vec(vec![10., 10.]);
24    let mut solver = GradientDescent::new(tol, x0);
25    // We define a callback to store iterates and function evaluations
26    let mut iterates = vec![];
27    let mut solver_callback = |s: &GradientDescent| {
28        iterates.push(s.x().clone());
29    };
30    // Running the solver
31    let max_iter_solver = 100;
32    let max_iter_line_search = 10;
33
34    solver
35        .minimize(
36            &mut ls,
37            f_and_g,
38            max_iter_solver,
39            max_iter_line_search,
40            Some(&mut solver_callback),
41        )
42        .unwrap();
43    // Printing the result
44    let x = solver.x();
45    let eval = f_and_g(x);
46    println!("x: {:?}", x);
47    println!("f(x): {}", eval.f());
48    println!("g(x): {:?}", eval.g());
49
50    // Plotting the iterates
51    let n = 50;
52    let start = -5.0;
53    let end = 5.0;
54    let plotter = Plotter3d::new(start, end, start, end, n)
55        .append_plot(&mut f_and_g, "Objective function", 0.5)
56        .append_scatter_points(&mut f_and_g, &iterates, "Iterates")
57        .set_layout_size(1600, 1000);
58    plotter.build("quadratic.html");
59}

More examples

Hide additional examples

examples/gradient_descent_example.rs (line 36)

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}