Merit Function Method For Structured Monotone Variational Inequalities

This paper presents a merit function method for structured monotone variational inequalities.Numerical results illustrates the efficiency of this method.1.Since 1960s,the theory and algorithms for finite-dimensional variational inequalities developed rapidly.Variational inequalities and complementarity problems have been developed an important field in applied mathematics.They have been widely used not only in nonlinear programming but in differential equation,mechanics,cybernetics,game theory,economic equilibrium theory,social and economic model,etc.Therefore,variational inequality and its application have become a focus in mathematics.2.In Chapter 3,we constructed a merit function based the model for structured monotone variational inequalities.We transformed the original problem to an optimization problem which possesses a very simple structure for calculation in our method.At last,we gave the global convergence condition.3.In Chapter 4,we introduced some algorithms for variational problems.Some numerical examples with ball constraints or box constraints were given.Numerical results verified the validity of the method provided in chapter three.