Difference between revisions of "ApCoCoA-1:Latte.Minimize"

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{{Version|1}}
 
<command>
 
<command>
 
<title>Latte.Minimize</title>
 
<title>Latte.Minimize</title>
 
<short_description>Minimizes the objective function over a polyhedral P given by a number of linear constraints.</short_description>
 
<short_description>Minimizes the objective function over a polyhedral P given by a number of linear constraints.</short_description>
 
<syntax>
 
<syntax>
Latte.Minimize(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, ObjectiveF: POLY):INT
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Latte.Minimize(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, ObjectiveF: POLY):LIST
 
</syntax>
 
</syntax>
  
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<item>@param <em>LesserEq</em>: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item>
 
<item>@param <em>LesserEq</em>: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints</item>
 
<item>@param <em>GreaterEq</em>: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints</item>
 
<item>@param <em>GreaterEq</em>: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints</item>
<item>@param <em>ObjectiveF</em>: A linear Polynomial</item>
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<item>@param <em>ObjectiveF</em>: A linear polynomial</item>
<item>@return The optimal value of the objective function</item>
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<item>@return A list: <tt>[[Optimal coordinates], Optimal solution, [Coeffs of objective function]]</tt></item>
 
</itemize>
 
</itemize>
  
 
<example>
 
<example>
Use S ::= QQ[x,y,z];
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Use S ::= QQ[x,y];
 
Equations := [];
 
Equations := [];
LesserEq := [x-1, x+y-1];
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LesserEq := [-x-2, x-y-24];
GreaterEq := [x,y];
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GreaterEq := [-x,-y];
ObjectiveF := x + z;
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ObjectiveF := x-2y;
 
Latte.Minimize(Equations, LesserEq, GreaterEq, ObjectiveF);
 
Latte.Minimize(Equations, LesserEq, GreaterEq, ObjectiveF);
  
[[0], <quotes>No optimal solution found</quotes>, [0]]
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[[-2, 0], -2, [1, -2]]
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
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<key>Minimize</key>
 
<key>Minimize</key>
 
<key>Latte.Minimize</key>
 
<key>Latte.Minimize</key>
<wiki-category>Package_latte</wiki-category>
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<wiki-category>ApCoCoA-1:Package_latte</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:10, 7 October 2020

This article is about a function from ApCoCoA-1.

Latte.Minimize

Minimizes the objective function over a polyhedral P given by a number of linear constraints.

Syntax

Latte.Minimize(Equations: LIST, LesserEq: LIST, GreaterEq: LIST, ObjectiveF: POLY):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

  • @param Equations: A list of linear polynomials, which are equivalent to the equality-part of the polyhedral constraints

  • @param LesserEq: A list of linear polynomials, which are equivalent to the lower or equal-part of the polyhedral constraints

  • @param GreaterEq: A list of linear polynomials, which are equivalent to the greater or equal-part of the polyhedral constraints

  • @param ObjectiveF: A linear polynomial

  • @return A list: [[Optimal coordinates], Optimal solution, [Coeffs of objective function]]

Example

Use S ::= QQ[x,y];
Equations := [];
LesserEq := [-x-2, x-y-24];
GreaterEq := [-x,-y];
ObjectiveF := x-2y;
Latte.Minimize(Equations, LesserEq, GreaterEq, ObjectiveF);

[[-2, 0], -2, [1, -2]]
-------------------------------