By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known ...By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known VASP code.The other was given by Eyert. We solve the Kohn-Sham equation by using a conventional outward/inward integration of the differential equation and then connect two parts of solutions at the classical turning points, which is different from the method of the matrix eigenvalue solution as used in the VASP code. Compared to Johnson＇s algorithm, the one proposed by Eyert needs fewer total iteration numbers.展开更多
In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent...In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function.展开更多
In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton met...In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61176080)
文摘By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known VASP code.The other was given by Eyert. We solve the Kohn-Sham equation by using a conventional outward/inward integration of the differential equation and then connect two parts of solutions at the classical turning points, which is different from the method of the matrix eigenvalue solution as used in the VASP code. Compared to Johnson＇s algorithm, the one proposed by Eyert needs fewer total iteration numbers.
文摘In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function.
文摘In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence.
