Synthesis of optimization algorithms by concatenating deterministic and autonomous algorithm components

This paper discusses a systematic approach to algorithm synthesis based on the use of problem model/algorithm schema pairs. A specific problem model, the intersection model, is examined, and the properties of several classes of associated algorithm schemas that employ the concatenation of deterministic algorithm components are presented. For those problems in which component algorithms can be formulated as continuous mappings, two algorithms are given in which algorithm components are utilized in a predetermined order. Two adaptive algorithms are introduced to remove the requirement for continuity. For all algorithms considered, monotonicity with respect to a surrogate map is required to insure desirable properties of convergence.