gurobi absolute value constraint

How to handle absolute value in Gurobi constraints

stackoverflow.com › questions › 58612670 › how-to-handle-absolute-value-in-gurobi-constraints

The abs_ function is part of the Gurobi Python API and does not work in an LP file. (When your LP file is read, the solver interprets your C3 constraint as a linear constraint with four variables with names abs_(v0, v1), abs_(v1, and v2).)

Also, note that absolute value constraints can only take the form var1 = abs_(var2). So you will have to define some auxiliary variables to model the constraint above.

In the Python API, you could model the constraint C3 as follows:

a = model.addVars(4, name="a")   # auxiliary variables
model.addConstr(a[0] == v0 - v1)
model.addConstr(a[1] == v1 - v2)
model.addConstr(a[2] == abs_(a[0]))
model.addConstr(a[3] == abs_(a[1]))

model.addConstr(a[2] + a[3] >= 10)

In the LP file, you can see the absolute value constraint in the General Constraints section:

General Constraints
 GC0: a[2] = ABS ( a[0] )
 GC1: a[3] = ABS ( a[1] )

Answer from Silke Horn on Stack Overflow

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How to handle absolute value in Gurobi constraints - Stack Overflow

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The abs_ function is part of the Gurobi Python API and does not work in an LP file. (When your LP file is read, the solver interprets your C3 constraint as a linear constraint with four variables with names abs_(v0, v1), abs_(v1, and v2).)

Also, note that absolute value constraints can only take the form var1 = abs_(var2). So you will have to define some auxiliary variables to model the constraint above.

In the Python API, you could model the constraint C3 as follows:

a = model.addVars(4, name="a")   # auxiliary variables
model.addConstr(a[0] == v0 - v1)
model.addConstr(a[1] == v1 - v2)
model.addConstr(a[2] == abs_(a[0]))
model.addConstr(a[3] == abs_(a[1]))

model.addConstr(a[2] + a[3] >= 10)

In the LP file, you can see the absolute value constraint in the General Constraints section:

General Constraints
 GC0: a[2] = ABS ( a[0] )
 GC1: a[3] = ABS ( a[1] )

Gurobi

support.gurobi.com › hc › en-us › community › posts › 23001326746001-Gurobi-Absolute-Value-Constraints

Gurobi- Absolute Value Constraints – Gurobi Help Center

Can I put the bound on the precision of the variable so that it only takes the desired values after the decimal places for solving the model? e.g x= 2.9001000000000015 but if I have to allow this to take only up to 7 decimal places, like x = 2.9001001? can it be possible to set the precision of the variable in Gurobi? Unfortunately, it is currently not possible to set individual variable tolerances. ... Re-optimize and check whether constraint violations improved without degrading the optimal solution value

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How to handle absolute value in Gurobi constraints – Gurobi Help Center

We introduce auxiliary variables \( y_0 = v_0 - v_1 \) and \( y_1 = v_1 - v_2 \). Then, we use variables \( z_0 = |y_0| \) and \( z_1 = |y_1| \) to represent the corresponding absolute value terms. \ abc.lp Maximize v0 + v1 + v2 Subject To R0: 3 v0 + v1 + v2 <= 72 R1: 2 v0 + 3 v1 + 2 v2 <= 80 R2: - v0 + v1 + y0 = 0 R3: - v1 + v2 + y1 = 0 R4: z0 + z1 >= 10 Bounds Generals v0 v1 v2 General Constraints GC0: z0 = ABS ( y0 ) GC1: z1 = ABS ( y1 ) End ... Thank you so much for your help. ... The absolute function in constraints works well in MATLAB +YALMIP. However, when I am trying to use the same constraint in PYOMO, Gurobi is not able to solve it.

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Abs Value – Gurobi Help Center

The abs_() function can only be used to set one decision variable equal to the absolute value of another. E.g.: ... You unfortunately can't use abs_() in any other type of constraint, like you try to do in the first example.

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support.gurobi.com › hc › en-us › community › posts › 360071098332-How-to-add-a-constraint-which-is-the-absolute-value-is-smaller-than-a-constant

How to add a constraint which is the absolute value is smaller than a constant? – Gurobi Help Center

I am now adding a constraint which contains a absolute value and a float constant. Here is an example: suppose that I have two variables x and y, which are added through m.addVar() variables: x, y · constraint: |x - y| < 0.7 · I tried to do · model.addConstr(gp.abs_(x - y) < 0.7) However, I got the error due to the mismatch of the types for comparison. How can I solve this problem? Thank you. 0 · 2 comments · Sort by Date Votes · Official comment · Simranjit Kaur · Gurobi Staff ·

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absolute value constraint on vectorised variable setting – Gurobi Help Center

These Var objects can be used in general constraint functions. E.g.: import gurobipy as gp m = gp.Model() x = m.addMVar(3) y = m.addMVar(3) # MVar objects are not currently integrated with general constraints # m.addConstr(y == gp.abs_(x)) does not work # Use corresponding Var objects instead for vx, vy in zip(x.tolist(), y.tolist()): m.addConstr(vy == gp.abs_(vx))

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Abs value constraint for MLinExpr – Gurobi Help Center

Depending on the values of the two matrices, the minimal value of the loss may be 0 (with x=0) or negative. I previosly tried to solve the optimization problem in Matlab using the Yalmip wrapper and a nonconvex solver (bmibnb), which works as expected. Now i have problems solving it in Python. Since the 1-Norm is not supported in the API, I try to model it as a sum of absolute values.

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docs.gurobi.com › projects › optimizer › en › current › reference › python › func_utility.html

Python General Constraint Helper Reference - Gurobi Optimizer Reference Manual

Gurobi general constraint helper functions - used in conjunction with overloaded operators and Model.addConstr or Model.addConstrs to build general constraints. abs_(argvar)# Used to set a decision variable equal to the absolute value of another decision variable.

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Model.addGenConstrAbs() - Gurobi Optimization

June 5, 2024 - An ABS constraint states that the resultant variable should be equal to the absolute value of the argument variable .

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docs.gurobi.com › projects › optimizer › en › current › concepts › modeling › constraints.html

Constraints - Gurobi Optimizer Reference Manual

The L-infinity norm is equal to the maximum absolute value of any operand. The L2 norm is equal to the square root of the sum of the squares of the operands. The L0 norm counts the number of non-zero values among the operands. Regarding the L2 norm, one obvious complication comes from the fact ...

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How to handle absolute value in objective function? – Gurobi Help Center

November 3, 2020 - A very detailed description of how to formulate the minimization of the absolute function can be found in the stackexchange post Converting absolute value program into linear program. Regarding the formulation \((a \cdot b - c) \cdot (a \cdot b - c)\). It is possible to formulate it with Gurobi, if you introduce an auxiliary variable \(z\) and the equality constraint \[ z = a \cdot b.\] Your problem would then read

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Absolute value, abs(), on Gurobi solver - Optimization (Mathematical) - Julia Programming Language