fminunc — Find unconstrained local minima in MATLAB and RunMat.

x = fminunc(fun, x0) minimizes a finite real scalar objective starting from binary64 x0. Scalar guesses return scalars, and vector or array guesses return solutions with the same shape as x0.

Syntax

x = fminunc(fun, x0)
x = fminunc(fun, x0, options)
[x, fval] = fminunc(fun, x0)
[x, fval] = fminunc(fun, x0, options)
[x, fval, exitflag] = fminunc(fun, x0)
[x, fval, exitflag] = fminunc(fun, x0, options)

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

Inputs

Returns

Returned values from fminunc depend on how many outputs the caller requests.

Errors

How fminunc works

• Uses a host-side BFGS quasi-Newton method with a strong-Wolfe line search.
• Strict compatibility mode rejects typed-integer or logical initial guesses, objective values, and supplied gradients. RunMat extension mode accepts those values when every integer converts exactly to binary64.
• Typed-integer option controls are a separately gated RunMat extension. Structural counts such as MaxIter and MaxFunEvals are validated as exact nonnegative integers rather than rounded through floating point.
• When SpecifyObjectiveGradient is false or omitted, gradients are estimated with forward finite differences.
• When SpecifyObjectiveGradient is true, the objective callback is called as [f, g] = fun(x) and g must contain one gradient entry per element of x.
• Options are supplied as a struct, usually from optimoptions or optimset. TolX, TolFun, MaxIter, MaxFunEvals, Display, Algorithm, and SpecifyObjectiveGradient are accepted.
• Supported Algorithm values are 'quasi-newton' and 'bfgs'; trust-region mode is not enabled in this implementation.
• Multi-output forms return x, fval, exitflag, output, grad, and an approximate Hessian.

Does RunMat run fminunc on the GPU?

The builtin registers ResidencyPolicy::GatherImmediately because BFGS iterations need scalar objective values, gradient vectors, and adaptive line-search decisions on the CPU.

Providers do not implement a direct fminunc hook; acceleration remains available inside user callback computations.

GPU memory and residency

fminunc is a host-side optimization sink. GPU-resident initial guesses are gathered before the solve, and objective callbacks may opt back into GPU work internally.

Examples

Minimize a quadratic vector objective

fun = @(x) sum((x - [1; 2; 3]).^2);
x = fminunc(fun, [0; 0; 0])

Expected output:

x =
    1.0000
    2.0000
    3.0000

Use an objective gradient

fun = @(x) deal(sum((x - [1; 2]).^2), 2*(x - [1; 2]));
opts = optimoptions('fminunc', 'SpecifyObjectiveGradient', true);
[x, fval, exitflag, output, grad] = fminunc(fun, [0; 0], opts)

Expected output:

x =
    1.0000
    2.0000

fval = 0
exitflag = 1

Using fminunc with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how fminunc changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how fminunc is executed, line by line, in Rust.

• View the source for fminunc in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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