Equation alignment of an optimization problem

Question

In the following excerpt of a write-up, I was wondering how to left-align \hat{L} and f on the second column of the first two lines. The best I could produce is below.

Thanks.

\documentclass{extbook}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\begin{document}
    \begin{equation*}
        \begin{aligned}
            &\text{maximize}   && \hat{L}(f) \\
            &\text{subject~to} & f &\in H_0^1[a,b], \\
            && \int_a^b f(x) \diff x &= 1, \\
            && f(x) &\geq 0  \text{ for all } x \in [a,b].
        \end{aligned}
    \end{equation*}
\end{document}

Do they need to line up with the integral on the third line? — Kenneth Odle, Jul 18 '23 at 19:02
Just out of idle curiosity: What's the (typographic) purpose of aligning the \in symbol in line 2, the = symbol in line 3, and the \geq symbol in line 4 ? — Mico, Jul 18 '23 at 19:50
@Mico: You can say "typographic preference". Your solution is also good, and I'm considering it. — AEW, Jul 18 '23 at 19:58

Mico · Answer 1 · 2023-07-18T19:35:48.007

Is a two-column layout ok? (What would be point of aligning the \in symbol on line 2, the = symbol on line 3, and the \geq symbol on line 4 with each other?)

Remove the \textstyle and \smash directives in line 3 if you want a large integral symbol.

\documentclass{extbook}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\begin{document}
\begin{alignat}{2}
  &\text{maximize}        && \hat{L}(f) \[\jot] % insert some whitespace padding
  &\text{subject to\quad} && f \in H_0^1 [a,b], \
  &                       && \textstyle\smash{\int_a^b} f(x)\diff x=1, \
  &                       && f(x)\ge0  \text{ for all $x\in[a,b]$}.
\end{alignat}
\end{document}

score 4 · Accepted Answer · answered Jul 18 '23 at 19:46

Just playing around with the placement of \hat{L}(f):

\documentclass{article}
\usepackage{mathtools}
\newcommand{\diff}{\mathop{}!\mathrm{d}}
\begin{document}
Original:
[
  \begin{aligned}
    &\text{maximize}   &                       & \hat{L}(f) \
    &\text{subject~to} &                     f &\in H_0^1[a,b], \
    &                  & \int_a^b f(x) \diff x &= 1, \
    &                  &                  f(x) &\geq 0  \text{ for all } x \in [a,b].
  \end{aligned}
]
Updated:
[
  \begin{aligned}
    &\text{maximize}   & \mathrlap{\hat{L}(f)}\phantom{f} \
    &\text{subject~to} &                      f &\in H_0^1[a,b], \
    &                  &  \int_a^b f(x) \diff x &= 1, \
    &                  &                   f(x) &\geq 0  \text{ for all } x \in [a,b].
  \end{aligned}
]
\end{document}

The placement of \hat{L}(f) is to the left of an f in a zero-width math box that is left-aligned (has a right overlap) using \mathrlap. This requires mathtools which loads amsmath.

Thanks, @Werner, for the solution. – AEW Jul 18 '23 at 19:49 — AEW, Jul 18 '23 at 19:49

score 2 · Answer 3 · answered Jul 19 '23 at 16:03

2

Using optidef package.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{optidef}
\begin{document}
\begin{maxi}<b>
{ }{ \hat{L}(f) }{}{}
\addConstraint { f \in H_0^1 [a,b] }{  }
\addConstraint {\int_a^b f(x),\mathrm{d}x }{=1}
\addConstraint {f(x)}{\geq 0  \textup{ for all } x \in [a,b].}
\end{maxi}
\end{document}

answered Jul 19 '23 at 16:03

Sebastiano

54,118

2

It is a bit amusing that you basically gave the same answer to the same question asker about 1 month ago. – Willie Wong Jul 19 '23 at 16:08
1

@WillieWong When I find maximize or minimize I always use optidef package :-). Thank you so much for your advice. – Sebastiano Jul 19 '23 at 16:12
1

Thank you, @Sebastiano, for your answer. – AEW Jul 19 '23 at 17:04
1

@AEW You're welcome. – Sebastiano Jul 19 '23 at 18:52

Equation alignment of an optimization problem

3 Answers3