An　explicit　exact　formula　is　derived　for　the　objective　function　of　the　dual　model　of　a　class　of　separable　convex　programming　problems.　It　makes　more　mature　and　efficient　methods　can　be　chose　to　solve　the　dual　model.　Therefore,　the　advantage　of　applying　the　duality　theory　of　nonlinear　programming　to　efficiently　solve　structural　topology　optimization　problems　is　fully　exploited.　The　research　work　is　rooted　in　that　the　gap　of　a　nonlinear　convex　programming　with　its　dual　programming　is　zero.　Solving　original　programming　can　be　equivalently　transformed　into　solving　its　dual　programming.　The　scale　of　the　solved　programming　can　usually　be　reduced　greatly.　But　an　explicit　relationship　is　not　existed　between　the　original　programming　and　dual　programming　has　affected　the　application　of　the　dual　solution　algorithm.　Fortunately,　the　programming　models　of　a　large　class　of　structural　optimization　problems,　including　the　continuum　topology　optimization,　are　convex　and　separable.　And　an　explicit　relationship　between　the　original　variables　and　their　dual　variables　is　existed;　therefore,　the　dual　solution　algorithm　has　become　one　of　the　effective　methods　for　38　years.　However,　the　objective　function　of　the　dual　problem　is　not　explicit　for　a　long　time.　It　is　because　the　dual　problem　is　a　parametric　minimization　problem　which　leads　to　the　objective　function　is　expressed　as　an　implicit　expression.　The　common　explicit　expression　for　the　dual　objective　function　is　a　two-order　approximation.　The　regular　thinking　tendency　that　the　dual　problem　is　too　diffcult　to　be　expressed　explicitly　and　can　only　be　expressed　approximately　is　breakthrough.　A　dual　programming　explicit　model　(DP-EM)　method　is　put　forward　for　the　topology　optimization　of　continuum　structures.　Comparison　of　computational　efficiency　among　the　DP-EM　method,　the　dual　sequential　quadratic　program　(DSQP)　method　and　the　method　of　moving　asymptotes　(MMA)　is　presented.　The　results　showed　that:　(1)　more　external　iterations　are　needed　for　the　MMA　algorithm　than　the　DP-EM　algorithm　and　DSQP　algorithm;　(2)　same　external　iterations　are　needed　for　the　DP-EM　algorithm　and　DSQP　algorithm,　but　internal　iterations　is　less　for　the　DP-EM　method.　It　shows　the　advantage　of　the　DP-EM　algorithm　due　to　its　explicit　dual　function.　©　2017,　Editorial　Office　of　Chinese　Journal　of　Theoretical　and　Applied　Mechanics.　All　right　reserved.