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fix formattazione di alcuni esercizi di teoria
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5 changed files with 33 additions and 45 deletions
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\title{Gran Compendio OLI}
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\title{Gran Compendio OLI}
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\author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}}
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\author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}}
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\date{2021\\V1.2.1}
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\date{2021\\V1.2.2}
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\begin{document}
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\begin{document}
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\maketitle
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\maketitle
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\subsection{PLC minimization}
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\subsection{PLC minimization}
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\noindent\fbox{%
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\noindent\fbox{%
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\parbox{\textwidth}{%
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\parbox{\textwidth}{%
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Given a PLC problem P in minimization form, with 2 constraints with sign ’≥’ and 1
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Given a PLC problem P in minimization form, with 2 constraints with sign '$\geqq$' and 1 constraint with sign '=', and 5 variables, consider the dual problem D:
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constraint with sign ’=’, and 5 variables, consider the dual problem D:
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\begin{enumerate}[label=\Alph*]
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\begin{enumerate}[label=\Alph*]
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\item | D has 3 variables
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\item | D has 3 variables
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and 5 constraints;
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and 5 constraints;
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\begin{enumerate}[label=\Alph*]
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\begin{enumerate}[label=\Alph*]
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\item | is used to solve linear programming problems with continuous variables;
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\item | is used to solve linear programming problems with continuous variables;
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\item | always uses the lowest-first strategy to explore the subproblems.;
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\item | always uses the lowest-first strategy to explore the subproblems.;
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\item | is used to solve NP-complete (“difficult”) problems; (d) terminates in a polynomial number of iterations;
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\item | is used to solve NP-complete (“difficult”) problems;
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\item | terminates in a polynomial number of iterations;
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\item | at each iteration uses the simplex algorithm to solve the current subproblem.
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\item | at each iteration uses the simplex algorithm to solve the current subproblem.
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\end{enumerate}
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\end{enumerate}
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}%
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}%
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\parbox{\textwidth}{%
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\parbox{\textwidth}{%
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Given a PLC problem with $n$ variables and $m$ constraints, a basic matrix is:
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Given a PLC problem with $n$ variables and $m$ constraints, a basic matrix is:
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\begin{enumerate}[label=\Alph*]
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\begin{enumerate}[label=\Alph*]
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\item | a collection of $m$ constraints; (b) none of the above answers.;
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\item | a collection of $m$ constraints;
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\item | a square $m$x$m$ matrix with value 1 on the main diagonal; \item | a collection of $n-m$ columns of the constraint matrix; \item | a square submatrix of the constraint matrix, that can be inverted.
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\item | none of the above answers.;
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\item | a square $m$x$m$ matrix with value 1 on the main diagonal;
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\item | a collection of $n-m$ columns of the constraint matrix;
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\item | a square submatrix of the constraint matrix, that can be inverted.
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\end{enumerate}
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\end{enumerate}
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}%
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}%
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}%
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}%
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