Termination Conditition of ALADIN Toolbox

[xinliang-dai]

The default tolerance parameter is set to 10^{-10}, but some simulations shows a comparable lower accuracy. Main factor might lay in termination condition of ALADIN Toolbox.

Termination condition of ALADIN Toolbox differs from original ALADIN paper in 2 ways:

• Termination check is activated right after NLP local-step in ALADIN paper. In contrast to the original paper, Toolbox uses a while-loop for iterative, which means the termination conditions in the Toolbox acts like a pre-condition for the while-loop.

• The sufficitent and necessary conditions of ALADIN paper consists of feasibility condition

  

  and duality condition

  

  However, there is only feasibility condition in the Toolbox. Lacking duality condition, or more specifically, lacking consideration of penalty parameter might be the main factors for comparable lower accuracy.

This topic needs further investigated.