Local search proximal algorithms as decision dynamics with costs to move

Acceptable moves for the “worthwhile-to-move” incremental principle are such that “advantages to move” are higher than some fraction of “costs-to-move”. When combined with optimization, this principle gives raise to adaptive local search proximal algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move. In this last case, one obtains a dynamic cognitive approach to Ekeland’s ǫ-variational principle. As a general property, introduction of costs-to-move in the algorithms yields robustness and stability properties. 2000 Mathematics Subject Classification: 49M37, 90B50, 90C25, 90C30, 90C31, 90C56, 91E10, 91E40, 91E45.