Outside of margin Equation

Question

I am working with Lyx and am trying to fit an equation in my margin as it is getting out side of the margin as can be seen in the below image.

I have tried to use the multiline enviornment but it still did not work. I have also looked at different questions but were not helpful.

Can someone help please?

Below is a screen shot of how I am inputting the formula and what I have used in LYX.

Answer 1

Here two possibilities: one with the aligned environment, nested in equation, ans using\MoveEqLeftfrommathtools, the other usesflalignand an *adhoc* alignment point. Both use the medium-size fractions (\mfrac) fromnccmath`for the numerical fractions, as I think it looks better:

\documentclass{article}

\usepackage{nccmath}
\usepackage{mathtools}

\begin{document}

\begin{equation}
\label{off-margin}
\begin{aligned}
 \MoveEqLeft -\ell (\beta _{0},\boldsymbol{\beta }) + \lambda \|\boldsymbol{\beta }\|_{1} = \\
 & \biggl[-\frac{1}{n}\biggl(\sum_{i = 1}^{n} (\beta _{0}x_{i0} + \mathbf{x}^T\boldsymbol{\beta })y_i-\log(1 + \exp(\beta _{0}x_{i0} + \mathbf{x}^T\boldsymbol{\beta }))\biggr)\biggr] \\
 \text{where} &\phantom{ + } \boldsymbol{\beta } = (\beta _{1},\dots, \beta _{p})^{T}\text{ and } x_{i0} = 1 \text{ for all }i.
\end{aligned}
\end{equation}

Next, we need to show that the negative log-likelihood function is convex. By showing convexity it means that a local minimum exists which is the global minimum…

\begin{flalign}
  \label{off-margin1}
-\ell (\beta _{0},\boldsymbol{\beta }) & + \lambda \|\boldsymbol{\beta }\|_{1} = \notag \\
 &\phantom{ + } \biggl[-\mfrac{1}{n}\biggl(\sum_{i = 1}^{n} (\beta _{0}x_{i0} + \mathbf{x}^T\boldsymbol{\beta })y_i-\log(1 + \exp(\beta _{0}x_{i0} + \mathbf{x}^T\boldsymbol{\beta }))\biggr)\biggr] \\%
 \text{where} &\phantom{ + } \boldsymbol{\beta } = (\beta _{1},\dots, \beta _{p})^{T}\text{ and } x_{i0} = 1 \text{ for all }i. \notag
\end{flalign}

\end{document}