Dimensional reduction in constrained global optimization on smooth manifolds

• Approach to reduce the dimension of search domains in constrained global optimization on smooth manifolds.
• More equality constraints => more dimensional reduction.
• Mappings under optimization do not need to be differentiable or even continuous.
• Optimization task is executed while keeping candidate points/populations within feasible submanifolds.
• The proposed paradigm may be employed jointly with an extensive family of already established metaheuristics.

This work introduces an approach aimed at reducing the dimension of search domains in constrained global optimization of real valued functions defined on smooth manifolds, and subject (also and mainly) to equality constraints. The functions expressing the cited constraints must satisfy certain smoothness conditions, and other types of restrictions are simultaneously possible, but the effect of dimensional reduction will be proportional to the number of equality constraints. The objective functions under study do not need to be differentiable or even continuous, and it is shown that the optimization task will be executed so that candidate points remain in the corresponding submanifolds, evolving there during the whole optimization process. The proposed paradigm may be employed jointly with an extensive family of already established metaheuristics. After introducing the fundamental ideas and establishing the theoretical basis, some examples will illustrate the effectiveness of the proposed method.

Figure optionsDownload as PowerPoint slide