Much　research　has　been　devoted　to　complex-variable　optimization　problems　due　to　their　engineering　applications.　However,　the　complex-valued　optimization　method　for　solving　complex-variable　optimization　problems　is　still　an　active　research　area.　This　paper　proposes　two　efficient　complex-valued　optimization　methods　for　solving　constrained　nonlinear　optimization　problems　of　real　functions　in　complex　variables,　respectively.　One　solves　the　complex-valued　nonlinear　programming　problem　with　linear　equality　constraints.　Another　solves　the　complex-valued　nonlinear　programming　problem　with　both　linear　equality　constraints　and　an　-1-norm　constraint.　Theoretically,　we　prove　the　global　convergence　of　the　proposed　two　complex-valued　optimization　algorithms　under　mild　conditions.　The　proposed　two　algorithms　can　solve　the　complexvalued　optimization　problem　completely　in　the　complex　domain　and　significantly　extend　existing　complex-valued　optimization　algorithms.　Numerical　results　further　show　that　the　proposed　two　algorithms　have　a　faster　speed　than　several　conventional　real-valued　optimization　algorithms.　©　2016　IEEE.