Two Optimization Algorithms Based On Filled Function And Stochastic Differential Equation

The filled function method is one of the effective methods established for solving global optimization problems.Among the methods for local optimization,the gradient projection method is widely used because of its simplicity and practicability.Due to excellent numerical results as evaluation criterion,the filter technique is regarded as one of the effective tools for optimization.In order to optimize the global optimization algorithm,this paper combines the filter technique with the filled function method,and presents a generalized filled function filter algorithm based on gradient projection for the non-convex global optimization problems with linear constraints.In this paper,a new generalized filled function is given and its characteristics are discussed,especially the performance on the boundary.Based on that the theoretical algorithm for global optimization with constraints with arbitrary initial points is proposed.And the properties and the reasonable disposal of boundary problems are proved.The numerical results are listed at last to show the effectiveness of the algorithm.In addition,from the point of view of random algorithms,gradient projection is introduced in the stochastic differential equation and projected stochastic differential equation is given.The performance of the random process on the boundary is discussed in detail.What's more,the relationship between the solution of the projected stochastic differential equation and the solution of the original constrained optimization problems is explained.In order to solve the global optimization problems with linear constraints,a projected algorithm based on stochastic differential equations is proposed and the convergence of the stochastic algorithm is proved.Finally,the numerical results are given to illustrate the effectiveness.