Studying consistent and inconsistent nonconvex feasibility problems on a sphere and a singleton using Douglas–Rachford algorithm

Key Points

• Solutions to nonconvex feasibility problems on a sphere were achieved using the Douglas–Rachford algorithm, and performance metrics showed promise in optimization tasks.
• Key features include successful convergence rates for the Douglas–Rachford algorithm in tackling inconsistent nonconvex situations on various geometric structures.
• Employing a specialized algorithm, the study provides insights into handling complex feasibility problems, including variations between spheres and singletons.
• These findings underscore new avenues for optimization research, with particular relevance to geometric problem-solving techniques.