The　optimality　criteria　(OC)　method　and　mathematical　programming　(MP)　were　combined　to　found　the　sectional　optimization　model　of　frame　structures.　Different　methods　were　adopted　to　deal　with　the　different　constraints.　The　stress　constraints　as　local　constraints　were　approached　by　zero-order　approximation　and　transformed　into　movable　sectional　lower　limits　with　the　Rill　stress　criterion.　The　displacement　constraints　as　global　constraints　were　transformed　into　explicit　expressions　with　the　unit　virtual　load　method.　Thus　an　approximate　explicit　model　for　the　sectional　optimization　of　frame　structures　was　built　with　stress　and　displacement　constraints.　To　improve　the　resolution　efficiency,　the　dual-quadratic　programming　was　adopted　to　transform　the　original　optimization　model　into　a　dual　problem　according　to　the　dual　theory　and　solved　iteratively　in　its　dual　space.　A　method　called　approximate　scaling　step　was　adopted　to　reduce　computations　and　smooth　the　iterative　process.　Negative　constraints　were　deleted　to　reduce　the　size　of　the　optimization　model.　With　MSC/Nastran　software　as　structural　solver　and　MSC/Patran　software　as　developing　platform,　the　sectional　optimization　software　of　frame　structures　was　accomplished,　considering　stress　and　displacement　constraints.　The　examples　show　that　the　efficiency　and　accuracy　are　improved.