The Improved Algorithm And Applied Research Of Penalty Function Method

Penalty function method takes up a very important position in optimization theory and numerical calculations, as an important method for the solving of nonlinear constrained optimization problem, it has experienced a development climax in the 1950s and 1960s and has gained a series of important achievements. Due to its operability and practicability, especially in recent years, with the wide application of computer technology, it has got great development. Until today, some scholars have begun to apply penalty function method to solve large industrial problems such as the power system, water dispatching system and automotive transmission system. They have made some encouraging preliminary results. The basic principle of penalty function method is that we construct a penalty function which is based on the characteristics of the restraint function and add it to the objective function, so we can get an augmented objective function and change the constrained optimization problem into the unconstrained optimization problem.Papers are as follows:First, we introduce the development process of optimization methods, the related concepts and theorem and briefly introduce the method of soving constrained optimization problem penalty function method.Secondly, we apply a penalty function method of a mixed-integer nonlinear programming to the production batch of drinks.Thirdly, we put forward two penalty function methods of solving quadratic programming problem: an improving logarithm barrier function method solve the convex quadratic programming problem and an improving exterior point penalty function matrix method solve a class of special quadratic programming problem.Finally, we implove a algorithm which has the merit of interior point penalty function and exterior point penalty function-mixed penalty function method, thus it speeds up the search, and we also apply this imploving algorithm to flood control allocation problem.