Enhanced optimization solver interfaces for Sage

This project aims at improving the optimization capabilities of SageMath by connecting SageMath to interfaces to optimization solvers that are maintained outside of the Sage project. The goal is mainly achieved by replacing existing templates for solver backends and adding backends of selected solvers as well as testing and documenting for them. Several stages of development will be involved in this project, including deciding which issues to work on, solver selection based on in-depth investigation, code implementation and modification, testing, documenting and logging. Some steps of these will be iterated over and over to achieve consensus and approval under peer review until finalized. In general, we hope that the implementations of this coding project will empower more advanced research and applications regarding optimization and solver interface integration. The project is expected to have a significant impact on the optimization capabilities of SageMath, making it a more powerful and flexible tool for mathematical research and education.