# Difference between revisions of "Line search methods"

Author names: Elizabeth Conger
Steward: Dajun Yue and Fengqi You

# Introduction

Line search methods are a group of algorithms that determine the minimum of a defined multivariable function by selecting a reasonable direction relative to the function that will provide a value closer to the absolute minimum of the function. This process is iterated using defined direction parameters and step sizes of travel. Varying these will change the "tightness" of the optimization.

# Section 2

Solution to 48 States Traveling Salesman Problem

# Section 3

$E=mc^2$

# Conclusion

$\begin{bmatrix} G(x,y) & 0 & -A(x)^T \\ 0 & Y & W \\ A(x) & -I & 0 \end{bmatrix} \begin{bmatrix} \Delta x \\ \Delta s \\ \Delta y \end{bmatrix} = \begin{bmatrix} -\nabla f(x) + A(x)^T y \\ \mu e - W Y e \\ -g(x) + s \end{bmatrix}$

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