Adaptive coordinate descent

The adaptive coordinate descent was shown to be competitive to the state-of-the-art evolutionary algorithms and has the following invariance properties: CMA-like Adaptive Encoding Update (b) mostly based on principal component analysis (a) is used to extend the coordinate descent method (c) to the optimization of non-separable problems (d).

The adaptive coordinate descent method reaches the target value after only 325 function evaluations (about 70 times faster than coordinate descent), that is comparable to gradient-based methods.

The algorithm has linear time complexity if update coordinate system every D iterations, it is also suitable for large-scale (D>>100) non-linear optimization.

First approaches to optimization using adaptive coordinate system were proposed already in the 1960s (see, e.g., Rosenbrock's method).

[4] For practical applications see,[5] where an adaptive coordinate descent approach with step-size adaptation and local coordinate system rotation was proposed for robot-manipulator path planning in 3D space with static polygonal obstacles.