Under the assumption condition of taking target function as an uniform convex function. We have proved that the LRKOPT has the global convergence and partial superlinear convergence.

In this paper, constructs the asset conversion function for given asset model with the transaction costs and discusses some properties of asset conversion by using Martingale and dual approaches.

Yang presented characterizations of quasiconvex functions, strictly quasiconvex functions, and strongly quasiconvex functions respectively under a certain set of conditions.