Text Formatting ⇒ Writing a code for optimization problem

[omkardpd]

Hi,

I was wondering if there is a standard code format available in LaTex for writing an optimization problem such as

Maximize f(x)
Subject to
Constraint 1 = 0
Constraint 2 = 0
...
...

I see a number of documents which have these problems which specify 'x' under the word 'Maximize' in the objective function. I was unable to find how to arrange these things. May I get some help in this regard?

Thank you in advance.

Omkar

[Juanjo]

Attach or link to an image showing what you would like to obtain.

[omkardpd]

Hi,

Thank you for the reply. I have attached a sample image. I am looking at the following two things specifically:
1. The decision variables written under "Max" and arrangement of the objective function next to "Max".
2. Alignment of the objective function and the constraints.

I tried "align" option, but did not get satisfactory results. I thought there might be a standard format available.

Regards,

Omkar

[Juanjo]

The following code may serve as a starting point for writing your own optimization problems:

Code: Select all

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\DeclareMathOperator*{\Max}{Max}

\begin{document}
Let us consider the following maximization problem:
\begin{align}
   &\Max_{P_1,P_h,q_1,q_h,q_m}
   \begin{aligned}[t]
      &n_1\bigl(P_1-cq_1^2+\alpha cf(q_m)\big) \\
      &\qquad+n_h \bigl(P_h-cq_h^2+\alpha cf(q_m)\big)
   \end{aligned} \notag \\
   &\text{subject to} \notag \\
   & v_1 (q_1+\beta_pq_m)-P_1\geq v_1(q_h-\beta_dq_m)-P_h, \\
   & v_h (q_h+\beta_pq_m)-P_h\geq v_h(q_1+\beta_dq_m)-P_1, \\
   & v_1 (q_1+\beta_pq_m)\geq P_1, \\
   & v_h (q_h-\beta_dq_m)\geq P_h, \\
   & q_h\geq0,\quad q_1\geq0,\quad q_h\geq q_m,\quad q_1\geq q_m,
      \quad q_m\geq0.\notag
\end{align}

\end{document}

[jesus]

A bit late but it might help other people looking for the same answer. The package optidef (https://www.ctan.org/pkg/optidef) was intended as the easy way to define optimization problems.

Code: Select all

\usepackage{optidef}
    \begin{mini}|l|
	  {w,u}{f(w)+ R(w+6x)}{}{}
	  \addConstraint{g(w_k)+h(w_k)}{=0,}{k=0,\ldots,N-1}
	  \addConstraint{l(w_k)}{=5u,\quad}{k=0,\ldots,N-1}
     \end{mini}

The package has several more options. Below some examples are provided. To have a completely overview of the features and options check the documentation http://ctan.cs.uu.nl/macros/latex/contr ... tidef.pdf.


Using a shorter description of minimize/subject to.

Code: Select all

\usepackage[short]{optidef}
    \begin{mini}
	  {w,u}{f(w)+ R(w+6x)}{}{}
	  \addConstraint{g(w_k)+h(w_k)}{=0,}{k=0,\ldots,N-1}
	  \addConstraint{l(w_k)}{=5u,\quad}{k=0,\ldots,N-1}
    \end{mini}

Breaking the objective accross several lines.

Code: Select all

\usepackage[long]{optidef}
    \begin{mini}
      {w,u}{f(w)+ R(w+6x)+ H(100w-x*w/500)}{}{}
      \breakObjective{-g(w^3-x^2*200+10000*w^5)}
      \addConstraint{g(w_k)+h(w_k)}{=0,}{k=0,\ldots,N-1}
      \addConstraint{l(w_k)}{=5u,\quad}{k=0,\ldots,N-1}
    \end{mini}

Multilabeling/no labeling:

Code: Select all

\begin{mini*}
		{w}{f(w)+ R(w+6x)}
		{}{}
		\addConstraint{g(w)}{=0}
	\end{mini*}

Code: Select all

\begin{mini!}
		{w}{f(w)+ R(w+6x)}
		{}{}
		\addConstraint{g(w)}{=0}
	\end{mini!}

Alignment position of constraints with respect to the objective:

Alternative 1

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\begin{mini}\[2\]
      {w}{f(w)+ R(w+6x)}
      {\label{eq:Ex1}}{}
      \addConstraint{g(w)+h(w)}{=0}
      \addConstraint{t(w)}{=0.}
    \end{mini}

Alternative 2

Code: Select all

\begin{mini}\[3\]
 		{w}{f(w)+ R(w+6x)}
 		{\label{eq:Ex1}}{}
 		\addConstraint{g(w)+h(w)}{=0}
 		\addConstraint{t(w)}{=0.}
 	\end{mini}

Alternative 3

Code: Select all

\begin{mini}\[4\]
 		{w}{f(w)+ R(w+6x)}
 		{\label{eq:Ex1}}{}
 		\addConstraint{g(w)+h(w)}{=0}
 		\addConstraint{t(w)}{=0.}
 	\end{mini}

Other optimization environments

argmini

Code: Select all

\begin{argmini}
		{w}{f(w)+ R(w+6x)}
		{}{}
		\addConstraint{g(w)}{=0}
	\end{argmini}

maxi

Code: Select all

\begin{maxi}
		{w}{f(w)+ R(w+6x)}
		{}{}
		\addConstraint{g(w)}{=0}
	\end{maxi}

argmaxi

Code: Select all

\begin{argmaxi}
		{w}{f(w)+ R(w+6x)}
		{}{}
		\addConstraint{g(w)}{=0}
	\end{argmaxi}

Full details on the different implementations above (and more details) can be found in the documentation: http://ctan.cs.uu.nl/macros/latex/contr ... tidef.pdf.