This article,by studying relations between the normal side-coloring and the total coloring of graph using some relative results about the normal side-coloring,presents several new results,and offers a feasible method in researching the total coloring of graph.

And, we also introduce the methods dealing with the Maratos effect, the modifications of the variable metric matrix, the consistency as well as the feasible methods in the constrained variable metric methods, etc.

And, we also introduce the methods dealing with the Maratos effect, the modifications of the variable metric matrix, the consistence as well as the feasible methods in the constrained variable metric methods, etc.

The superlinearly convergent feasible methods for nonlinearly constrained optimization problems are an important research subject in both theory and practice.

This paper presents a class of feasible methods containing some of parameters for solving nonlinear inequality constrained optimization problem.

At the same time,the traditional feasible direction method(FDM) was improved.

In this paper, a feasible direction method is used to resolve problems of which the storage space is limited, the least quantity of purchase is no less than the starting point and different goods must be placed separately.

Furthermore,the results of comparative calculation show that the new method can considerably improve the rate of convergence for the feasible direction method.