- Difficulty to guarantee convergence to the global optima
- Reduction of the problem to its effective subspace
- Solving of reduced subproblems
- Finding of global optimal solutions for applications of neural networks, complex engineering and physical simulation
Various applications of neural networks and complex engineering and physical simulation, such as climate modelling, use global optimization techniques which consist in finding the global optimal solution of a given objective function with potential multiple local optima. The ability to guarantee convergence to the global optima is in general a very hard task.
A particular family of problems belongs to the bound-constrained global optimization of functions with low effective dimensionality, which only vary over a subspace and are constant along a linear subspace. However, the reduction of the problem to its effective subspace is not immediate as the constant subspace is generally unknown.
The authors propose a generic algorithm framework, which repeatedly solves reduced subproblems within random low-dimensional subspaces using any global, and even local, solver in the subproblem. In particular, one such solver being employed and tested is Artelys Knitro which the authors have found to be flexible and easy to use.