In　this　paper,　we　propose　two　fast　complex-valued　optimization　algorithms　for　solving　complex　quadratic　programming　problems:　1)　with　linear　equality　constraints　and　2)　with　both　an　l1-norm　constraint　and　linear　equality　constraints.　By　using　Brandwood＇s　analytic　theory,　we　prove　the　convergence　of　the　two　proposed　algorithms　under　mild　assumptions.　The　two　proposed　algorithms　significantly　generalize　the　existing　complex-valued　optimization　algorithms　for　solving　complex　quadratic　programming　problems　with　an　l1-norm　constraint　only　and　unconstrained　complex　quadratic　programming　problems,　respectively.　Numerical　simulations　are　presented　to　show　that　the　two　proposed　algorithms　have　a　faster　speed　than　conventional　real-valued　optimization　algorithms.　©　2013　IEEE.