A Minimax αβ Relaxation for Global Optimization

Abstract

Local minima make search and optimization harder. In this paper, we give a new global optimization approach, minimax aαβ relaxation, to cope with the pathological behavior of local minima. The minimax a αβ relaxation interplays a dual step minimax local to global optimization, an iterative local to global information propagation, and an adaptive local to global algorithm transition, within a parallel processing framework. In minimax αβ relaxation, a controls the rate of local to global information propagation and β controls the rate of algorithm transition from local to global optimization. Compared to the existing optimization approaches such as simulated annealing and local search, the minimax β relaxation demonstrates much better convergence performance for certain classes of constrained optimization problems.¹