Shuguang Wang ¹, Guozhong Zhao ¹, Luobin Xu ¹, Dezhi Guo ¹, Shuyan Sun ¹

History matching is an inverse problem of partial differential equation on mathematics. We adopt the constrained non-linear optimization to handle this problem, defining the objective function as the weighted square sum of differences between the wells simulation values and the corresponding observation values. We develop an optimization computing program that include Zoutendijk feasible direction methodQuasi-Newton method (BFGS) and improved Nelder-Mead simplex method, combined with a black-oil simulator, and discuss the convergence characters of algorithms in case studies about determining average porosity and directional permeability, determining low permeability strip between two wells and determining oil-water relative permeability curves.