Abstract: In this paper,we propose and prove following results:1.an expansion“criteria”of improving conservative approkimation and corresponding theorms;2.an approkimateEORCT(expansion of original/reciprocal variables based on cumulative informations attwo points)and its advantage of identical convex or concave character with primal function;3.a dual optimization method by using EORCT approximation and numerical collvegencyof its application to truss structures;4.relating convergent theorms of the optimizationmethol