The Application Of Stochastic Differential Equation In The Linear Constrained Nonconvex Global Optimization

Based on stochastic differential equations,three stochastic diffusion algorithms are proposed to solve nonconvex global optimization problems with linear constraints.The first algorithm is based on the effective constraint set method to transform the inequality-constraint problem into a finite series of equality-constraint subproblem,and then use the intermittent diffusion algorithm to solve the unconstrained problem on the hyperplane,and then find the global optimal solution.The second algorithm is based on the barrier function method.The barrier function method always starts from the interior point in the iteration and keeps searching in the feasible region.The original objective function is replaced by the objective function with penalty function,and the constrained optimization problem is transformed into the unconstrained problem.The third algorithm is based on the exterior penalty function method.Similar to the barrier function method,the objective function with penalty function is used to replace the original objective function,and the constrained optimization problem is transformed into an unconstrained problem.We focus on the theoretical proof of convergence of the three algorithms,and carry out numerical experiments,list the numerical results to show the effectiveness of the three algorithms.