Katana.jl Documentation

Katana.jl is a MathProgBase solver for Convex NonLinearPrograms (NLPs). Katana.jl solves NLPs via the Extended Cutting-Plane (ECP) method, which combines an Linear Programming solver with a cutting-plane generator to solve Convex NLPs. Katana.jl is well suited for large-scale Convex NLPs where most of the constraints are linear and the nonlinear constraints are sparse.

Example use

Katana can be used as a solver within a JuMP model. Consider the following non-linear program:

using Katana, JuMP, GLPKMathProgInterface

# use Katana with default parameters and GLPK as internal LP solver
katana = KatanaSolver(GLPKSolverLP())

m = Model(solver=katana)

# square-root cone constraint, non-linear constraint intersection example:
@variable(m, x, start=0.1)
@variable(m, y, start=0.1)
@variable(m, z)

@objective(m, Min, x+y)
@NLconstraint(m, sqrt(x^2 + y^2) <= z-0.25)
@constraint(m, x^2 + y^2 <= -z + 1)

solve(m)

For details on solver parameters, see the Library documentation.

Customising Katana for your use case

Katana is designed with modularity in mind. To that end, although the default cutting plane algorithm creates separating hyperplanes by performing a single iteration of Newton-Raphson around the optimal solution found by the linearised model, other separation oracles can be substituted through Katana's Separators API.

In addition, you may see benefits to substituting a proprietary linear solver (e.g. Gurobi) for improved stability and speed.

Katana appears to also be well-suited for computing decently tight lower bounds on non-linear objective functions. By specifying the obj_eps parameter to the KatanaSolver, you can control the solver's stopping criterion to be a 'good enough' objective value.

Consult the User Manual for more.