数学附录 16凸规划: Assume that f and g are differentiable functions defined on a convex set XoRn and non- decreasing in each variable. Assume that f is quasi concave and g is quasi-convex, and that f(O=gO=0. Then both of the primal and the dual convex programming problems (where c> and kare constants): maxf(x),S.T.g(x)≤c, min g(X), s.T. f(x)2k, have optimal solutions. The solution of the primal (resp. the dual) problem is a tangent point of g(x) =c (resp f(x)=k) with a level set of f (resp g).数学附录 • 16 凸规划: Assume that f and g are differentiable functions defined on a convex set Xn and non￾decreasing in each variable. Assume that f is quasi￾concave and g is quasi-convex, and that f(O)=g(O)=0. Then both of the primal and the dual convex programming problems (where c>0 and k>0 are constants): max f(x), S.T. g(x)<c, min g(x), S.T. f(x)>k, have optimal solutions. The solution of the primal (resp.the dual) problem is a tangent point of g(x)=c (resp. f(x)=k) with a level set of f (resp. g)