Based　on　mathematical　programming　theory,　the　reciprocal　programming　is　defined　as　a　pair　of　programming　which　objective　and　constraint　functions　are　changed　each　other.　After　that,　it　is　pointed　out　that　reciprocal　programming　and　dual　programming　seem　similar　but　there　are　five　differences　between　them:　(1)　the　difference　in　whether　they　are　the　same　problem　or　not;　(2)　the　difference　in　whether　there　exists　a　dual　gap　or　not;　(3)　the　difference　in　the　number　of　design　variables;　(4)　the　difference　between　single-objective　and　multi-objective　problems;　(5)　the　difference　between　reasonable　and　unreasonable　problems.　Finally,　based　on　the　definition　of　the　reciprocal　programming,　the　structural　topology　optimization　model　is　examined;　and　following　results　are　obtained:　(1)　from　this　perspective,　it　is　clear　that　there　exists　indeed　unreasonable　models　that　have　been　used　in　structural　optimization;　(2)　a　way　to　correct　the　unreasonable　model　and　make　it　reasonable　is　put　forward;　(3)　the　reasons　that　the　minimizing　compliance　model　with　volume　constraint　(MCVC　for　short)　is　unreasonable　are　presented;　(4)　according　to　the　theory　presented　in　this　paper,　the　MCVC　model　is　actually　the　m-aspect　of　reciprocal　programming,　so　its　corresponding　s-aspect　is　established,　that　is,　the　minimizing　volume　model　with　multiple　compliance　constraints　(MVCC　for　short);　(5)　the　physical　interpretation　and　algorithm　of　structural　compliance　constraints　in　the　MVCC　model　are　presented;　and　the　concepts　and　methods　of　global　stress　constraint　in　the　ICM　(Independent　continuous　and　mapping)　method　are　demonstrated;　(6)　numerical　examples　show　the　differences　between　the　MCVC　and　MVCC　model　as　a　pair　of　reciprocal　programming　and　verify　the　rationality　of　the　MVCC　model.　Different　optimized　topologies　are　obtained　for　the　MCVC　model　with　different　volume　constraints　and　different　weighting　coefficients　for　multiple　load　cases.　But　a　unique　optimized　topology　can　be　achieved　by　the　MVCC　model　with　compliance　constraints　under　multiple　load　case.　©　2019,　Chinese　Journal　of　Theoretical　and　Applied　Mechanics　Press.　All　right　reserved.