S4 is a solver for semidefinite optimization problems written in MATLAB. It accepts problems in SDPA Format and will print intermediate information regarding solver progress at each iteration. This solver is naively implemented and memory inefficient, therefore a "simple solver" for "small SDPs". However, with less than 500 lines total of well-commented code, this project is ideal for learning about semidefinite optimization. The algorithm used is described in "Solving semidefinite-quadratic-linear programs using SDPT3" by Tutuncu, Toh, and Todd and further implementation details are described in "On the Nesterov-Todd Direction in Semidefinite Programming" by the same authors.
The main solver is contained in S4.m and all other files are helper functions which are called during each iteration of the solver. To invoke the solver, call S4(filename), where filename is in SDPA format. Several example problems are provided in the problems directory, and more can be found online here.