The Composition of Modified Reflection Operators and Their Fixed Point Sets

The modified reflection operator plays a crucial role in optimization, particularly in algorithms designed to solve constrained optimization problems. By effectively transforming feasible solutions while maintaining their viability within defined constraints, this operator enables smoother navigation through the solution space. It enhances convergence rates and stability in iterative methods, such as projected gradient descent and proximal algorithms. In this paper, we investigate the fixed point sets of the compositions of three modified reflection operators onto linear closed subspaces. We also derive formulas for the compositions under different parameters.