Variable Metric Method for Unconstrained Multiobjective Optimization Problems

In this paper,we propose a variable metric method for unconstrained multiobjective optimization problems(MOPs).First,a sequence of points is generated using different positive definite matrices in the generic framework.It is proved that accumulation points of the sequence are Pareto critical points.Then,without convexity assumption,strong convergence is established for the proposed method.Moreover,we use a common matrix to approximate the Hessian matrices of all objective functions,along which a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate.Finally,several numerical results demonstrate the effectiveness of the proposed method.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

A New Three-Level Hierarchical Control Algorithm for Large-Scale Systems

This paper presents a new three-level hierarchical control parallel algorithm for large-scale systems by spatial and time decomposition. The parallel variable metric (PVM)method is found to be promising third-level algorithm. In the subproblems of second-level, the constraints of the smaller subproblem requires that the initial state of a subproblem equals the terminal state of the preceding subproblem. The coordinating variables are updated using the modified Newton method. the low-level smaller subproblems are solved in parallel using extended differential dynamic programmeing (DDP). Numerical result shows that comparing with one level DDP. the PVM /DDP algorithm obtains significant speed-ups.

Stochastic back analysis of permeability coefficient using generalized Bayesian method

Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms withrevised search direction. Under some inexact line searches, we prove that the algorithms areglobally convergent for continuously differentiable functions and the rate of convergence of thealgorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.

THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION

In this paper, we discuss the convergence of Broyden algorithms for the functions which are non-twice differentiable, but have LC gradient. We prove that the rate of convergence of the algorithms is linear for uniformly convex functions. We also demonstrate that under some mild conditions the algorithms are superlinsarly convergent.