Semidefinite programming is a method used to solve complex optimization problems by minimizing a linear function while ensuring that a combination of symmetric matrices meets certain criteria. This method is useful in various fields like engineering and combinatorial optimization. Despite being more general than linear programming, semidefinite programs are not significantly harder to solve. Interior-point methods, commonly used in linear programming, have been adapted for semidefinite programs with good results. Overall, semidefinite programming offers a versatile and efficient approach to solving optimization problems in real-world applications.