The　combination　of　space　mapping　(SM)　and　response　surface　methodology　(RSM)　provides　a　good　solution　for　the　mapping　of　response　surfaces　from　the　low-fidelity　model　to　the　high-fidelity　model.　A　class　of　optimization　problems　can　be　formulated　as　quadratic　programming　models,　which　is　convenient　for　finding　the　optimal　design,　and　simplifies　the　parameter　extraction　procedure　in　the　implementation　of　SM　simultaneously.　The　computational　efforts　involved　in　the　repetitive　analyses　can　be　cut　down.　The　new　algorithm　makes　the　implementation　of　successive　RSM　more　feasible.　The　numerical　examples　show　that　good　efficiency　and　precision　can　be　achieved.