Please use the latest enhanced version of CAT based on our recent paper "A simple and practical adaptive trust-region method."

CAT

This package is the implementation of a consistently adaptive trust-region method (called CAT) for finding stationary points of nonconvex functions with L-Lipschitz Hessians and bounded optimality gap.

One-time setup

Install Julia 1.6.0 or later. From the root directory of the repository, run:

$ julia --project=scripts -e 'import Pkg; Pkg.instantiate()'

Validate setup by running the unit tests:

$ julia --project=scripts test/run_tests.jl

Experimental results

The full tables of results can be found under the results directory

Running

Learning linear dynamical systems

To test our solver on learning linear dynamical system, please use the script:

solve_learning_problem.jl

To see the meaning of each argument:

$ julia --project=scripts scripts/solve_learning_problem.jl --help

Here is a simple example:

$ julia --project=scripts scripts/solve_learning_problem.jl --output_dir ./scripts/benchmark/results/learning_problem --d 3 --T 5 --σ 0.1 --instances 5

Matrix completion problem

To test our solver on matrix completion problem, please use the script:

solve_matrix_completion.jl

To see the meaning of each argument:

$ julia --project=scripts scripts/solve_matrix_completion.jl --help

Here is a simple example:

$ julia --project=scripts scripts/solve_matrix_completion.jl --output_dir ./scripts/benchmark/results/matrix_completion --λ_1 0.001 --λ_2 0.001 --instances 5

CUTEst test set

To test our solver on CUTEst test set, please use the script:

solve_cutest.jl

To see the meaning of each argument:

$ julia --project=scripts scripts/solve_cutest.jl --help

Here is a simple example:

$ julia --project=scripts scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --solver CAT

Complexity hard example

To test our solver on the complexity hard example from Cartis et.al paper "On the complexity of steepest descent, newton’s and regularized newton’s methods for nonconvex unconstrained optimization problems", please use the script:

solve_hard_example.jl

To see the meaning of each argument:

$ julia --project=scripts scripts/solve_hard_example.jl --help

Here is a simple example:

$ julia --project=scripts scripts/solve_hard_example.jl --output_dir ./scripts/benchmark/results/hard_complexity_example --tol_opt 1e-3 --r_1 1.5

Plots for CUTEst test set

$ julia --project=scripts scripts/plot_CUTEst_results.jl --output_dir ./scripts/benchmark/results/cutest

Instructions for reproducing our experiments

Learning linear dynamical systems

$ julia --project=scripts scripts/solve_learning_problem.jl --output_dir ./scripts/benchmark/results/learning_problem --d 4 --T 50 --σ 0.01 --instances 60

Matrix completion problem

$ julia --project=scripts scripts/solve_matrix_completion.jl --output_dir ./scripts/benchmark/results/matrix_completion --λ_1 0.01 --λ_2 0.01 --instances 10

CUTEst test set

$ julia --project=scripts scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --solver CAT

$ julia --project=scripts scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --solver CAT --θ 0.0

$ julia --project=scripts scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --solver NewtonTrustRegion

Complexity hard example

$ julia --project=scripts scripts/solve_hard_example.jl --output_dir ./scripts/benchmark/results/hard_complexity_example --tol_opt 1e-3 --r_1 1.5