Algorithm Gurobi uses to solve general convex optimization

Answered

Miranda

• December 09, 2020 17:57

Hello,

I am wondering which algorithm/optimizer Gurobi uses to solve 'general' convex optimization (linear objective with quadratic and linear constraints)? Is Gurobi using interior point algorithm?

Is there any algorithm could ensure the optimal solution for 'general' convex optimization (linear objective with quadratic and linear constraints) to be the extreme point? If so, how could I change the solver/algorithm that Gurobi uses to solve my model?

Thanks. 

0

• 

  Jaromił Najman

  Gurobi Staff

  • December 10, 2020 13:36

  Hi Miranda,

  Gurobi uses an interior point algorithm with predictor and corrector steps and a barrier objective function. The algorithm terminates when the difference between the primal and dual objective value reaches some given threshold. For QCPs, this threshold is defined by BarQCPConvTol and by BarConvTol for LPs.

  For LPs, the Crossover algorithm is used to obtain an extreme point as a solution point. This is not possible for QCPs due to the nonlinear constraints, which may force the optimal solution point away from an extreme point of the polyhedron defined by the remaining linear constraints.

  Best regards,
  Jaromił

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