When working with Julia, you may encounter the error message “Gurobi objective q not psd for convex quadratic problem”. This error typically occurs when using the Gurobi solver to solve a convex quadratic optimization problem. In this article, we will explore three different ways to solve this issue.
Option 1: Adjusting Gurobi Parameters
One possible solution is to adjust the parameters of the Gurobi solver. By default, Gurobi assumes that the objective function is positive semi-definite (psd). However, in some cases, the objective function may not satisfy this condition. To address this, you can set the parameter “NonConvex” to 2, which allows Gurobi to handle non-convex objectives.
using JuMP
using Gurobi
model = Model(Gurobi.Optimizer)
set_optimizer_attribute(model, "NonConvex", 2)
# Define your optimization problem here
optimize!(model)
This approach modifies the Gurobi solver’s behavior to handle non-convex objectives. However, it is important to note that this may impact the solver’s performance and solution quality.
Option 2: Reformulating the Problem
If adjusting the Gurobi parameters does not resolve the issue, another option is to reformulate the problem. This involves transforming the original problem into an equivalent form that satisfies the positive semi-definite condition.
One possible reformulation is to add a small positive constant to the diagonal elements of the objective’s Hessian matrix. This ensures that the matrix becomes positive semi-definite. Here’s an example of how you can implement this:
using JuMP
using Gurobi
model = Model(Gurobi.Optimizer)
# Define your optimization problem here
# Reformulate the objective function
@variable(model, x)
@objective(model, Min, x)
# Add a small positive constant to the diagonal elements of the Hessian matrix
@constraint(model, diag_const[i=1:n] => H[i,i] >= 1e-6)
optimize!(model)
This approach modifies the objective function to ensure that the Hessian matrix is positive semi-definite. However, it may introduce a small bias to the optimization problem.
Option 3: Using a Different Solver
If the previous options do not provide a satisfactory solution, you can consider using a different solver that can handle non-convex objectives. For example, the Mosek solver supports non-convex optimization problems.
using JuMP
using Mosek
model = Model(Mosek.Optimizer)
# Define your optimization problem here
optimize!(model)
Using a different solver may provide better performance and solution quality for non-convex problems. However, it is important to note that different solvers may have different licensing requirements and computational costs.
In conclusion, the best option depends on the specific problem and requirements. Adjusting Gurobi parameters may be the simplest solution, but it may impact performance. Reformulating the problem can ensure positive semi-definiteness, but it introduces a small bias. Using a different solver may provide better performance, but it may come with additional licensing and computational costs. Consider these factors when choosing the most suitable solution for your problem.