In　this　paper,　we　propose　a　complex-valued　neural　dynamical　method　for　solving　a　complex-valued　nonlinear　convex　programming　problem.　Theoretically,　we　prove　that　the　proposed　complex-valued　neural　dynamical　approach　is　globally　stable　and　convergent　to　the　optimal　solution.　The　proposed　neural　dynamical　approach　significantly　generalizes　the　real-valued　nonlinear　Lagrange　network　completely　in　the　complex　domain.　Compared　with　existing　real-valued　neural　networks　and　numerical　optimization　methods　for　solving　complex-valued　quadratic　convex　programming　problems,　the　proposed　complex-valued　neural　dynamical　approach　can　avoid　redundant　computation　in　a　double　real-valued　space　and　thus　has　a　low　model　complexity　and　storage　capacity.　Numerical　simulations　are　presented　to　show　the　effectiveness　of　the　proposed　complex-valued　neural　dynamical　approach.　©　2014　Elsevier　Ltd.