fminunc

Unconstrained nonlinear minimization.

📝Syntax

x = fminunc(fun, x0)
x = fminunc(fun, x0, options)
x = fminunc(problem)
[x, fval, exitflag, output, grad, hessian] = fminunc(___)

📥Input Arguments

Parameter	Description
fun	Objective function returning a real scalar. With gradient options enabled, it can also return the gradient and Hessian.
x0	Initial scalar, vector or matrix point.
options	Options created with optimoptions or optimset.
problem	Structure with fields objective, x0, solver and options.

📤Output Arguments

Parameter	Description
x	Computed minimizer.
fval	Objective value at x.
exitflag	Termination indicator.
output	Diagnostic structure with iterations, funcCount, stepsize, algorithm, firstorderopt and message.
grad	Gradient at x.
hessian	Approximate or user supplied Hessian at x.

📄Description

fminunc minimizes a scalar nonlinear objective without constraints.

The default quasi-newton algorithm uses BFGS, DFP, steepest descent, or limited-memory BFGS depending on HessianApproximation and legacy HessUpdate options. The trust-region algorithm uses user gradients, optional objective Hessians, Hessian multiply functions and truncated conjugate gradients.

Accepted display modes are off, none, final, final-detailed, notify, notify-detailed, iter and iter-detailed.

💡Examples

Minimize a quadratic polynomial.

fun = @(x) 3*x(1)^2 + 2*x(1)*x(2) + x(2)^2 - 4*x(1) + 5*x(2);
[x, fval] = fminunc(fun, [1, 1])

Use a gradient with the trust-region algorithm.

function [f, g] = rosenwithgrad(x)
  f = 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
  g = [-400*(x(2)-x(1)^2)*x(1) - 2*(1-x(1)); 200*(x(2)-x(1)^2)];
end
opts = optimoptions('fminunc', 'Algorithm', 'trust-region', 'SpecifyObjectiveGradient', true);
x = fminunc(@rosenwithgrad, [-1; 2], opts)

🔗See Also

fmincon optimoptions fminsearch

Used Functions

optimoptions optimset

📚Bibliography

Broyden, C. G., The convergence of a class of double-rank minimization algorithms, IMA Journal of Applied Mathematics, 1970. Fletcher, R., Practical Methods of Optimization, Wiley, 1987. Liu, D. C. and Nocedal, J., On the limited memory BFGS method for large scale optimization, Mathematical Programming, 1989. Nocedal, J. and Wright, S. J., Numerical Optimization, Springer, 2006.

🕔Version History

Version	Description
2.0.0	initial version

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