An improved nonlinear conjugate gradient method with an optimal property

Conjugate gradient methods have played a special role in solving large scale nonlinear problems. Recently, the author and Dai proposed an efficient nonlinear conjugate gradient method called CGOPT, through seeking the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method. In this paper, we make use of two types of modified secant equations to improve CGOPT method. Under some assumptions, the improved methods are showed to be globally convergent. Numerical results are also reported.

Research of the Conductive Structure of Crust and the Upper Mantle beneath the South-Central Tibetan Plateau

With the super-wide band magnetoteiluric sounding data of the JUong （吉隆）-Cuoqin （措勤） profile （named line 800） which was completed in 2001 and the Dingri （定日）-Cuomai （措迈） profile （named line 900） which was completed in 2004, we obtained the strike direction of each MT station by strike analysis, then traced profiles that were perpendicular to the main strike direction, and finally obtained the resistivity model of each profile by nonlinear conjugate gradients （NLCG） inversion. With these two models, we described the resistivity structure features of the crust and the upper mantle of the center-southern Tibetan plateau and its relationship with Yalung Tsangpo suture： the upper crust of the research area is a resistive layer with resistivity value range of 200-3 000 Ω.m. The depth of its bottom surface is about 15-20 km generally, but the bottom surface of resistive layer is deeper in the middle of these two profiles. At llne 900, it is about 30 km deep, and even at line 800, it is about 38 km deep. There is a gradient belt of resistivity at the depth of 15-45 km, and a conductive layer is beneath it with resistivity even less than 5 Ω.m. This conductive layer is composed of individual conductive bodies, and at the south of the Yalung Tsangpo suture, the conductive bodies are smaller with thickness about 10 km and lean to the north slightly. However, at the north of the Yalung Tsangpo suture, the conductive bodies are larger with thickness about 30 km and also lean to the north slightly. Relatively, the conductive bodies of line 900 are thinner than those of line 800, and the depth of the bottom surface of line 900 is also shallower. At last, after analyzing the effect factors to the resistivity of rocks, it was concluded that the very conductive layer was caused by partial melt or connective water in rocks. It suggests that the middle and lower crust of the center-southern Tibetan plateau is very thick, hot, flabby, and waxy.

A CONJUGATE GRADIENT METHOD FOR DISCRETE-TIME OUTPUT FEEDBACK CONTROL DESIGN

In this paper, the discrete-time static output feedback control design problem is con- sidered. A nonlinear conjugate gradient method is analyzed and studied for solving an unconstrained matrix optimization problem that results from this optimal control prob- lem. In addition, through certain parametrization to the optimization problem an initial stabilizing static output feedback gain matrix is not required to start the conjugate gradi- ent method. Finally, the proposed algorithms are tested numerically through several test problems from the benchmark collection.

A COMPUTATIONAL APPROACH FOR OPTIMAL CONTROL SYSTEMS GOVERNED BY PARABOLIC VARIATIONAL INEQUALITIES

Iterative techniques for solving optimal control systems governed by parabolic varia-tional inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equations and nonlinear conjugate gradient methods to solve the discrete optimal control problem. Convergence results and numerical experiments are presented.