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针对优化问题的宏

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针对优化问题的宏

这个问题是在 xparse 命令中使用数组环境。有人建议我为扩展单独提出一个问题。非常感谢 egreg 的帮助。我还有两个功能想要实现，我想知道我是否可以从社区获得更多帮助。

具体来说，我希望支持框约束和枚举约束。在 egreg 使用 LaTeX3 给出解决方案之前，我的约束命令是一个带有签名的宏mmmggo。前三个参数表示标准约束；第四和第五个参数表示框约束中的附加信息；第六个参数表示枚举约束的枚举。我尝试让这些功能正常工作，如下所示（失败的部分已被注释掉）。

关于我做出某些选择的动机，有几点需要说明：我希望使约束在使用中可读，这就是为什么我更喜欢使用下面给出的约束命令来格式化约束；如果没有枚举任何约束，我希望防止打印用于设置枚举的\qquad参数，以保持问题的水平居中。我认为框约束问题基本已解决（我总是可以在第三个参数中包含框约束的附加信息，如下所示）。但是，我真的很想能够

  1. 将枚举作为可选参数，并且
  2. 当没有使用枚举约束时，抑制\qquad用于设置枚举（以保留优化问题的水平居中）。

\documentclass{article}
    \usepackage{amsmath}
    \usepackage{array}
    \usepackage{xparse}

    \ExplSyntaxOn
        % allocate the variables for an optimization problem
        \tl_new:N \l_optprob_operator_tl
        \tl_new:N \l_optprob_variable_tl
        \tl_new:N \l_optprob_objective_tl
        \tl_new:N \l_optprob_constraints_tl

        % define the keys
        \keys_define:nn{optprob}
        {
            operator   .tl_set:N = \l_optprob_operator_tl,
            variable   .tl_set:N = \l_optprob_variable_tl,
            objective  .tl_set:N = \l_optprob_objective_tl,
            constraint .code:n   = \optprob_add_constraint:nnnnnn #1,
            % constraint .code:n   = \constraint{#1}
        }

        \NewDocumentCommand{\optimizationproblem}{m}
        {
            % clear the variables
            \tl_clear:N \l_optprob_operator_tl
            \tl_clear:N \l_optprob_variable_tl
            \tl_clear:N \l_optprob_objective_tl
            \tl_clear:N \l_optprob_constraints_tl

            % get the keys
            \keys_set:nn{optprob}{#1}

            % print the optimization problem
            \tl_if_empty:NTF \l_optprob_objective_tl
            {
                % feasibility problem
                \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l}
                    \l_optprob_constraints_tl
                \end{array}
            }
            {
                % optimization problem
                \begin{array}{c@{{}\mathrel{:}{}}l}
                    \displaystyle\operatorname*{\l_optprob_operator_tl}\sb{\l_optprob_variable_tl} &
                        \l_optprob_objective_tl \\[2ex]
                    \tl_if_empty:NF \l_optprob_constraints_tl
                    {
                        % constrained optimization problem
                        \textnormal{subject~to} &
                            \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l}
                                \l_optprob_constraints_tl
                            \end{array}
                    }
                \end{array}
            }
        }

        \NewDocumentCommand{\constraint}{mmmggo}
        {
            \IfValueTF{#4}
            {
                \IfValueTF{#6}
                {
                    #1 & #2 & #3 #4 #5 & \qquad #6 \\
                }
                {
                    #1 & #2 & #3 #4 #5 \\
                }
            }
            {
                \IfValue{#6}
                {
                    #1 & #2 & #3 & \qquad #6 \\
                }
                {
                    #1 & #2 & #3 \\
                }
            }
        }

        % helper function to process the constraints
        \cs_new_protected:Npn \optprob_add_constraint:nnnnnn #1 #2 #3 #4
        {
            \tl_put_right:Nn \l_optprob_constraints_tl {#1 & #2 & #3 & \qquad #4 \\}
        }
    \ExplSyntaxOff

\begin{document}

\[
    \optimizationproblem
    {
        operator   = minimize,
        variable   = x \in \mathbf{R}^{n},
        objective  = c^{T} x,
        constraint = {A_{i} x}{=}{b_{i}}{i = 1 , \ldots , m},
        % constraint = {A_{i} x}{=}{b_{i}}[i = 1 , \ldots , m],
        constraint = {F_{j} x}{\leq}{g_{j}}{j = 1 , \ldots , m},
        % constraint = {F_{j} x}{\geq}{g_{j}}[j = 1 , \ldots , m],
        constraint = {0}{\leq}{x \leq 1}{},
        % constraint = {0}{\leq}{x}{\leq}{1},
    }
\]

\end{document}

答案1

我的建议是添加两个新键；可以添加一些检查以确保它们遵循关联的constraint键。

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{xparse}

\ExplSyntaxOn
% allocate the variables for an optimization problem
\tl_new:N \l_optprob_operator_tl
\tl_new:N \l_optprob_variable_tl
\tl_new:N \l_optprob_objective_tl
\tl_new:N \l_optprob_constraints_tl

% define the keys
\keys_define:nn{optprob}
 {
  operator   .tl_set:N = \l_optprob_operator_tl,
  variable   .tl_set:N = \l_optprob_variable_tl,
  objective  .tl_set:N = \l_optprob_objective_tl,
  constraint .code:n   = \optprob_add_constraint:nnn #1,
  cinfo      .code:n   = \optprob_add_info:n { #1 },
  cnumber    .code:n   = \optprob_add_number:n { #1 },
 }

\NewDocumentCommand{\optimizationproblem}{m}
 {
  % clear the variables
  \tl_clear:N \l_optprob_operator_tl
  \tl_clear:N \l_optprob_variable_tl
  \tl_clear:N \l_optprob_objective_tl
  \tl_clear:N \l_optprob_constraints_tl

  % get the keys
  \keys_set:nn{optprob}{#1}

  % print the optimization problem
  \tl_if_empty:NTF \l_optprob_objective_tl
   {
    % feasibility problem
    \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l}
       \l_optprob_constraints_tl
    \end{array}
   }
   {
    % optimization problem
    \begin{array}{c@{{}\mathrel{:}{}}l}
      \displaystyle\operatorname*{\l_optprob_operator_tl}\sb{\l_optprob_variable_tl} &
        \l_optprob_objective_tl \\[2ex]
      \tl_if_empty:NF \l_optprob_constraints_tl
       {
        % constrained optimization problem
        \textnormal{subject~to} &
        \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l}
          \l_optprob_constraints_tl
        \end{array}
       }
    \end{array}
   }
 }
% helper function to process the constraints
\cs_new_protected:Npn \optprob_add_constraint:nnn #1 #2 #3
 {
  \tl_if_empty:NF \l_optprob_constraints_tl
   { \tl_put_right:Nn \l_optprob_constraints_tl { \\ } }
  \tl_put_right:Nn \l_optprob_constraints_tl { #1 & #2 & #3 }
 }
\cs_new_protected:Npn \optprob_add_info:n #1
 {
  \tl_put_right:Nn \l_optprob_constraints_tl { \quad (#1) }
 }
\cs_new_protected:Npn \optprob_add_number:n #1
 {
  \tl_put_right:Nn \l_optprob_constraints_tl { & \qquad #1 }
 }
\ExplSyntaxOff

\begin{document}

\[
\optimizationproblem
 {
  operator   = minimize,
  variable   = x \in \mathbf{R}^{n},
  objective  = c^{T} x,
  constraint = {A_{i} x}{=}{b_{i}},
    cinfo    = {i = 1 , \ldots , m},
  constraint = {F_{j} x}{\leq}{g_{j}},
    cinfo    = {j = 1 , \ldots , m},
 }
\]

\[
\optimizationproblem
 {
  operator   = minimize,
  variable   = x \in \mathbf{R}^{n},
  objective  = c^{T} x,
  constraint = {A_{i} x}{=}{b_{i}},
    cinfo    = {i = 1 , \ldots , m},
    cnumber  = 1,
  constraint = {F_{j} x}{\leq}{g_{j}},
    cinfo    = {j = 1 , \ldots , m},
    cnumber  = 2,
 }
\]

\end{document}

cinfo如果值包含逗号，请不要忘记值周围的括号。

在此处输入图片描述

答案2

@egreg 非常感谢您的帮助！我最终对您提供的答案做了一个小改动，我想将其作为我原始问题的最终答案发布。我还希望您能检查我的工作。在您的解决方案中，字段cinfo没有完全对齐，所以我想在数组中创建一个单独的列来保存这些字段。但是，处理字段的函数cnumber需要知道cinfo字段是否已针对当前约束进行处理，以便将cnumber字段放在正确的列中。我使用变量来实现这一点\l_optprob_cinfo_flag_tl。如果我的解决方案的风格或逻辑有任何问题，请告诉我，再次感谢您帮助我按照我想要的方式设置这个宏。

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{xparse}

\ExplSyntaxOn
% allocate the variables for an optimization problem
\tl_new:N \l_optprob_operator_tl
\tl_new:N \l_optprob_variable_tl
\tl_new:N \l_optprob_objective_tl
\tl_new:N \l_optprob_constraints_tl
\tl_new:N \l_optprob_cinfo_flag_tl

% define the keys
\keys_define:nn{optprob}
 {
  operator   .tl_set:N = \l_optprob_operator_tl,
  variable   .tl_set:N = \l_optprob_variable_tl,
  objective  .tl_set:N = \l_optprob_objective_tl,
  constraint .code:n   = \optprob_add_constraint:nnn #1,
  cinfo      .code:n   = \optprob_add_info:n { #1 },
  cnumber    .code:n   = \optprob_add_number:n { #1 },
 }

\NewDocumentCommand{\optimizationproblem}{m}
 {
  % clear the variables
  \tl_clear:N \l_optprob_operator_tl
  \tl_clear:N \l_optprob_variable_tl
  \tl_clear:N \l_optprob_objective_tl
  \tl_clear:N \l_optprob_constraints_tl
  \tl_clear:N \l_optprob_cinfo_flag_tl

  % get the keys
  \keys_set:nn{optprob}{#1}

  % print the optimization problem
  \tl_if_empty:NTF \l_optprob_objective_tl
   {
    % feasibility problem
    \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l@{}l}
       \l_optprob_constraints_tl
    \end{array}
   }
   {
    % optimization problem
    \begin{array}{c@{{}\mathrel{:}{}}l}
      \displaystyle\operatorname*{\l_optprob_operator_tl}\sb{\l_optprob_variable_tl} &
        \l_optprob_objective_tl \\[2ex]
      \tl_if_empty:NF \l_optprob_constraints_tl
       {
        % constrained optimization problem
        \textnormal{subject~to} &
        \begin{array}[t]{@{}r@{}>{{}}c<{{}}@{}l@{}l@{}l}
          \l_optprob_constraints_tl
        \end{array}
       }
    \end{array}
   }
 }
% helper function to process the constraints
\cs_new_protected:Npn \optprob_add_constraint:nnn #1 #2 #3
 {
  \tl_if_empty:NF \l_optprob_constraints_tl
   { \tl_put_right:Nn \l_optprob_constraints_tl { \\ } }
  \tl_put_right:Nn \l_optprob_constraints_tl { #1 & #2 & #3 }
  \tl_clear:N \l_optprob_cinfo_flag_tl
 }
\cs_new_protected:Npn \optprob_add_info:n #1
 {
  \tl_put_right:Nn \l_optprob_constraints_tl { & \quad (#1) }
  \tl_put_right:Nn \l_optprob_cinfo_flag_tl {set flag}
 }
\cs_new_protected:Npn \optprob_add_number:n #1
 {
    \tl_if_empty:NT \l_optprob_cinfo_flag_tl
    {
        \tl_put_right:Nn \l_optprob_constraints_tl { & }
    }   
  \tl_put_right:Nn \l_optprob_constraints_tl { & \qquad #1 }
 }
\ExplSyntaxOff

\begin{document}

\[
\optimizationproblem
 {
  operator   = minimize,
  variable   = x \in \mathbf{R}^{n},
  objective  = c^{T} x,
  constraint = {A_{i} x}{=}{b_{i}},
    cinfo    = {i = 1 , \ldots , m},
  constraint = {F_{j} x}{\leq}{g_{j}},
    cinfo    = {j = 1 , \ldots , m},
 }
\]

\[
\optimizationproblem
 {
  operator   = minimize,
  variable   = x \in \mathbf{R}^{n},
  objective  = c^{T} x,
  constraint = {A_{i} x}{=}{b_{i}},
    cinfo    = {i = 1 , \ldots , m},
    cnumber  = 1,
  constraint = {F_{j} x}{\leq}{g_{j}},
    cinfo    = {j = 1 , \ldots , m},
    cnumber  = 2,
 }
\]

\[
\optimizationproblem
 {
  operator   = minimize,
  variable   = x \in \mathbf{R}^{n},
  objective  = c^{T} x,
  constraint = {A_{i} x}{=}{b_{i}},
    cinfo    = {i = 1 , \ldots , m},
    cnumber  = 1,
  constraint = {F x}{\leq}{g},
    cnumber  = 2,
 }
\]

\end{document}

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