A Filled-Filter Function Method For Solving Nonlinear Programming Problem

In this paper, we have studied the method for solving nonlinear global optimization problems by using filter-filled function. Filled function method is one of effective methods for solving global optimization problems, which can effectively solve the optimization problems to find better than the current local minimum point. Filter method is one method of penalty-parameter-free, it is widely applied in solving local minimum point for its excellent numerical results. In this paper, we combine filled function and filter method to solve nonlinear programming problems for first time. The second chapter discusses the filled function method to solve unconstrained global optimization problems, while the third chapter discusses the filled function method to solve constrained global optimization problems as follows:The second chapter, proposes a new filled function, analyzes and proves its filling properties; constructs the search direction and proves it is decline direction of the objective function and filled function; gives algorithm based on the filter, and shows the effectiveness and feasibility of algorithm through numerical experiments.The third chapter, expands filter-filled function method to solve the constrained global optimization problems. Constructs a new auxiliary filled function, proves property of the function. Adds restoration and recoveries in order to control problem of viable outside the domain boundary when iteration, and discusses the minimum point after recovery; lists the results of numerical experiments at last.