strong Wolfe line search with cubic interpolation. Can be used by using strongwolfe=1 in BFGS. For non smooth functions, this is not recommended for BFGS. Use weak line search instead. recommended for use with CG, where strong Wolfe condition needed for convergence analysis

1 2 | ```
linesch_sw(fn, gr, x0, d, f0 = fn(x0),
grad0 = gr(x0), c1 = 0, c2 = 0.5, fvalquit = -Inf, prtlevel = 0)
``` |

`fn` |
A function to be minimized. fn(x) takes input as a vector of parameters over which minimization is to take place. fn() returns a scaler. |

`gr` |
A function to return the gradient for fn(x). |

`x0` |
initial point |

`d` |
search direction |

`f0` |
fn(x0) |

`grad0` |
gr(x0) |

`c1` |
Wolfe parameter for the sufficient decrease condition |

`c2` |
c2: Wolfe parameter for the WEAK condition on directional derivative |

`fvalquit` |
quit if f gets below this value. |

`prtlevel` |
prints messages if this is 1 |

returns a list containing the following fields:

`alpha` |
steplength satisfying Wolfe conditions |

`x` |
x0 + alpha*d |

`f` |
f(x0 + alpha d) |

`grad` |
(grad f)(x0 + alpha d) |

`fail` |
0 if both Wolfe conditions satisfied, or falpha < fvalquit 1 if one or both Wolfe conditions not satisfied but an interval was found bracketing a point where both satisfied -1 if no such interval was found, function may be unbounded below |

`nsteps` |
number of steps taken in lszoom |

Copyright (c) 2010 Michael Overton for Matlab code and documentation, with permission converted to R by Abhirup Mallik (and Hans W Borchers).

Numerical Optimization by Jorge Nocedal and Stephen J. Wright

1 2 3 4 5 6 7 8 9 10 11 12 13 |

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