Abstarct: This research focuses on the investigation and analysis of methods for solving convex quadratic programming problems. Initially, solution approaches for this class of problems under equality constraints are presented. Subsequently, by generalizing the problem to a broader context, algorithms baxsed on the two main approaches of active-set and interior-point methods are developed and examined for solving convex quadratic programming problems with more general constraints. It will be demonstrated in this study that each of these algorithms exhibits superior efficiency and convergence speed under specific problem conditions. The application of an algorithm outside its optimal designed scope may lead to numerical challenges and a significant increase in the number of iterations required to attain the optimal solution. Hence, identifying the optimal application domain for each method constitutes a crucial part of the analysis presented in this research.