The Research On Quartic Minimization Based On Proximal And Difference Of Convex Method

In this thesis,a method for quartic minimization over the sphere is DC programming.We improved the DC algorithm based on the proximal algorithm and propose two algorithms,p DCA and a DCA.We prove that the global convergence and convergence speed of the algorithm reach at least sublinear convergence.Numerical experimental results show that compared with the general DC algorithm and the HOPM,p DCA and a DCA require less time and the optimality of the calculation solution has been improved.This thesis first introduces the research status of tensor decomposition and best rank one approximation problems,and shows that the quartic minimization over the sphere is essentially a class of best rank one approximation problems.Then,the principles of the proximal algorithm and the convex difference algorithm are introduced.It shows the similarity and combinability of the two algorithms.The idea of proximal operator is adopted when constructing the convex difference decomposition of the problem,so that when solving the subproblem of the algorithm,only the projection needs to be calculated,and the iterative process is optimized.Then we analyze and prove that the sequence generated by the algorithm converges to a local optimal solution of the objective function...