The theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry.ampampnbspWhen unknown or uncertain data in an optimization problem is replaced with parameters one obtains a multiparametric optimization problem whose optimal solution comes in the form of a function of the parameters.The theory and methodology presented in this work allows one to solve both Linear Programs and convex Quadratic Programs containing parameters in any location within the problem data as well as multiobjective optimization problems with any number of convex quadratic or linear objectives and linear constraints. Applications of these classes of problems are extremely widespread ranging from business and economics to chemical and environmental engineering.