Linesearch

Algorithm

i) Set iteration counter $k=0$, and make an initial guess, $\backslash mathbf\{x\}\_0$ for the minimum.

ii) Compute a descent direction $\backslash mathbf\{p\}\_k$.

iii) Choose $\backslash alpha\_k$ to 'loosely' minimize $\backslash phi(\backslash alpha)=f(\backslash mathbf\{x\}\_k+\backslash alpha\backslash mathbf\{p\}\_k)$ over $\backslash alpha\backslash in\backslash mathbb\; R$.

iv) Update $\backslash mathbf\{x\}\_\{k+1\}=\backslash mathbf\{x\}\_k+\backslash alpha\_k\backslash mathbf\{p\}\_k$, $k=k+1$.

If $\backslash |\backslash nabla\; f(\backslash mathbf\{x\}\_k)\backslash |\backslash leq$tolerance, STOP.

Else, goto ii).

Reference

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