Constraint satisfaction problem (CSP) for inequalities of vectors
I have two vectors $Y= (y_1, y_2, ldots, y_m)^T$ and $S= (s_1, s_2,ldots, s_m)^T$, where all entries in $Y$ and $S$ being positive integers. $Y$ is defined by $Y = A + B cdot X$, where $A$ is a constant $m$-vector, $B$ is a constant $m times n$ matrix and $X$ is a variable $n$-vector.
Given $S$, I want to find all the possible values of $X = (x_1, x_2, ldots, x_n)^T$ such that $Y neq S$ using linear integer programming.
I thought of using the following constraint satisfaction problem (CSP) by adding the variable $z_j$ such that $z_j = |y_j - s_j|$ to check that at least for one entry $j$ we have $y_j neq s_j$:
$$Y = A + B cdot X geqslant vec{0},\
z_j = |y_j - s_j|,quad forall j in 1, cdots, m\
sum_{j=1}^{m} z_j geq 1.$$
But I have a problem with the absolute value. What should I do to achieve this?
linear-algebra linear-programming integer-programming constraint-programming
edited Nov 28 '18 at 5:07
Saad
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
add a comment |
I have two vectors $Y= (y_1, y_2, ldots, y_m)^T$ and $S= (s_1, s_2,ldots, s_m)^T$, where all entries in $Y$ and $S$ being positive integers. $Y$ is defined by $Y = A + B cdot X$, where $A$ is a constant $m$-vector, $B$ is a constant $m times n$ matrix and $X$ is a variable $n$-vector.
Given $S$, I want to find all the possible values of $X = (x_1, x_2, ldots, x_n)^T$ such that $Y neq S$ using linear integer programming.
I thought of using the following constraint satisfaction problem (CSP) by adding the variable $z_j$ such that $z_j = |y_j - s_j|$ to check that at least for one entry $j$ we have $y_j neq s_j$:
$$Y = A + B cdot X geqslant vec{0},\
z_j = |y_j - s_j|,quad forall j in 1, cdots, m\
sum_{j=1}^{m} z_j geq 1.$$
But I have a problem with the absolute value. What should I do to achieve this?
linear-algebra linear-programming integer-programming constraint-programming
edited Nov 28 '18 at 5:07
Saad
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31
add a comment |
I have two vectors $Y= (y_1, y_2, ldots, y_m)^T$ and $S= (s_1, s_2,ldots, s_m)^T$, where all entries in $Y$ and $S$ being positive integers. $Y$ is defined by $Y = A + B cdot X$, where $A$ is a constant $m$-vector, $B$ is a constant $m times n$ matrix and $X$ is a variable $n$-vector.
Given $S$, I want to find all the possible values of $X = (x_1, x_2, ldots, x_n)^T$ such that $Y neq S$ using linear integer programming.
I thought of using the following constraint satisfaction problem (CSP) by adding the variable $z_j$ such that $z_j = |y_j - s_j|$ to check that at least for one entry $j$ we have $y_j neq s_j$:
$$Y = A + B cdot X geqslant vec{0},\
z_j = |y_j - s_j|,quad forall j in 1, cdots, m\
sum_{j=1}^{m} z_j geq 1.$$
But I have a problem with the absolute value. What should I do to achieve this?
linear-algebra linear-programming integer-programming constraint-programming
edited Nov 28 '18 at 5:07
Saad
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
I have two vectors $Y= (y_1, y_2, ldots, y_m)^T$ and $S= (s_1, s_2,ldots, s_m)^T$, where all entries in $Y$ and $S$ being positive integers. $Y$ is defined by $Y = A + B cdot X$, where $A$ is a constant $m$-vector, $B$ is a constant $m times n$ matrix and $X$ is a variable $n$-vector.
Given $S$, I want to find all the possible values of $X = (x_1, x_2, ldots, x_n)^T$ such that $Y neq S$ using linear integer programming.
I thought of using the following constraint satisfaction problem (CSP) by adding the variable $z_j$ such that $z_j = |y_j - s_j|$ to check that at least for one entry $j$ we have $y_j neq s_j$:
$$Y = A + B cdot X geqslant vec{0},\
z_j = |y_j - s_j|,quad forall j in 1, cdots, m\
sum_{j=1}^{m} z_j geq 1.$$
But I have a problem with the absolute value. What should I do to achieve this?
linear-algebra linear-programming integer-programming constraint-programming
linear-algebra linear-programming integer-programming constraint-programming
edited Nov 28 '18 at 5:07
Saad
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
edited Nov 28 '18 at 5:07
Saad
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
edited Nov 28 '18 at 5:07
Saad
19.7k92352
edited Nov 28 '18 at 5:07
Saad
19.7k92352
edited Nov 28 '18 at 5:07
Saad
19.7k92352
19.7k92352
asked Nov 28 '18 at 4:45
I.Saadaoui
113
asked Nov 28 '18 at 4:45
I.Saadaoui
113
asked Nov 28 '18 at 4:45
I.Saadaoui
113
113
look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31
add a comment |
look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31
look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31
add a comment |
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look up how to model piecewise linear functions by using binary variables
– LinAlg
Nov 28 '18 at 13:11
@LinAlg thank you for this answer. I am new to this field can you please give me more hints.
– I.Saadaoui
Nov 28 '18 at 14:10
section 7.6 of download.aimms.com/aimms/download/manuals/AIMMS3_OM.pdf
– LinAlg
Nov 28 '18 at 14:31