A New Class of Nonlinear Conjugate Gradient Methods with Global Convergence Properties

非线性共轭梯度法由于其迭代简单和储存量小,且搜索方向不需要满足正割条件,在求解大规模无约束优化问题时占据及其重要的地位.提出了一类新的共轭梯度法,其搜索方向是目标函数的下降方向.若假设目标函数连续可微且梯度满足Lipschitz条件,线性搜索满足Wolfe原则,讨论了所设计算法的全局收敛性.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

Global Convergence of an Extended Descent Algorithm without Line Search for Unconstrained Optimization

In this paper, we extend a descent algorithm without line search for solving unconstrained optimization problems. Under mild conditions, its global convergence is established. Further, we generalize the search direction to more general form, and also obtain the global convergence of corresponding algorithm. The numerical results illustrate that the new algorithm is effective.

ON THE GLOBAL CONVERGENCE OF CONJUGATE GRADIENT METHODS WITH INEXACT LINESEARCH

In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.

GLOBAL CONVERGENCE OF THE GENERAL THREE TERM CONJUGATE GRADIENT METHODS WITH THE RELAXED STRONG WOLFE LINE SEARCH

The global convergence of the general three term conjugate gradient methods with the relaxed strong Wolfe line search is proved.

Local convergence zones or discontinuous lines in the Taklimakan Desert, Northwest China

In order to study convergence zones or discontinuous lines formed locally in the Taklimakan Desert,we analyzed available MODIS images onboad TERRA or AQUA satellite for ten cases:29 March 2002,14 April 2002;2 January 2003;21 April 2003;26 March 2004;28 April 2004;30 January 2005;25 June 2005;3 December 2005;and 26 July 2006.We used weather maps published by the Japan Mete-orological Agency for the Asia and Pacific region at 500 hPa,700 hPa and 850 hPa,at 00Z and 12Z to analyze the meteorological conditions occurring in each case.We estimated the positions of air streams,convergence zones or discontinuous lines between them,and thermal conditions on the maps and con-firmed the presence of cumulus and cumulonimbus clouds through satellite images in particular.After a review of previous studies,this paper introduced the results of the present study.Closed warm areas in the Taklimakan Desert and on the Tibetan Plateau and local convergence zones or discontinuous lines in the Taklimakan Desert were discussed together with their diurnal changes,using composite maps of the ten cases.Along the long axis of the desert the convergence zones or discontinuous lines normally extend 70-80 km in a west-east direction,but are suspected to exceed 100 km in extreme cases.On the other hand,the convergence zones or discontinuous lines extending in a north-south direction on the southern fringe of the desert have a length of 40-60 km.The closed warm areas show clear diurnal changes,but they were not detected at the 500 hPa level.An example of a clear convergence zone running in a north-south direction on 26 July 2006 was presented in detail with corresponding satellite images.

The global convergence of the non-quasi-Newton methods with non-monotone line search

The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved. Numerical experiments showed that the non-monotone line search was more effective.

Several New Line Search Methods and Their Convergence

In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding original ones and give an adequate initial step size at each iteration. It is proved that the resulting line search algorithms have global convergence under some mild conditions. It is also proved that the search direction plays an important role in line search methods and that the step size approaches mainly guarantee global convergence in general cases. The convergence rate of these methods is also investigated. Some numerical results show that these new line search algorithms are effective in practical computation.

Convective Initiation by Topographically Induced Convergence Forcing over the Dabie Mountains on 24 June 2010

The initiation of convective cells in the late morning of 24 June 2010 along the eastward extending ridge of the Dabie Mountains in the Anhui region, China, is studied through numerical simulations that include local data assimilation. A primary convergence line is found over the ridge of the Dabie Mountains, and along the ridge line several locally enhanced convergence centers preferentially initiate convection. Three processes responsible for creating the overall convergence pattern are identified. First, thermally-driven upslope winds induce convergence zones over the main mountain peaks along the ridge, which are shifted slightly downwind in location by the moderate low-level easterly flow found on the north side of a Mei-yu front. Second, flows around the main mountain peaks along the ridge create further convergence on the lee side of the peaks. Third, upslope winds develop along the roughly north-south oriented valleys on both sides of the ridge due to thermal and dynamic channeling effects, and create additional convergence between the peaks along the ridge. The superposition of the above convergence features creates the primary convergence line along the ridge line of the Dabie Mountains. Locally enhanced convergence centers on the primary line cause the initiation of the first convection cells along the ridge. These conclusions are supported by two sensitivity experiments in which the environmental wind （dynamic forcing） or radiative and land surface thermal forcing are removed, respectively. Overall, the thermal forcing effects are stronger than dynamic forcing given the relatively weak environmental flow.

Feasible SQP Descent Method for Inequality Constrained Optimization Problems and Its Convergence

In this paper,the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented,and under weaker conditions of relative,we proofed the new method still possesses global convergence and its strong convergence.The numerical results illustrate that the new methods are valid.

Convergence Analysis on a Class of Nonmonotone Conjugate Gradient Methods without Sufficient Decrease Condition

In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.

A Descent Gradient Method and Its Global Convergence

Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new descent gradient method based on the LS method.It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search.Finally,we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP^+method.

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUTSUFFICIENT DECREASE CONDITION

Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

A MIXED SUPERLINEARLY CONVERGENT ALGORITHM WITH NONMONOTONE SEARCH FOR CONSTRAINED OPTIMIZATIONS

In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.

SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

Method of Lines for Third Order Partial Differential Equations

The method of lines is applied to the boundary-value problem for third order partial differential equation. Explicit expression and order of convergence for the approximate solution are obtained.

A Line Search Algorithm for Unconstrained Optimization

It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.

Research on Narrowband Line Spectrum Noise Control Method Based on Nearest Neighbor Filter and BP Neural Network Feedback Mechanism

Thefilter-x least mean square(FxLMS)algorithm is widely used in active noise control(ANC)systems.However,because the algorithm is a feedback control algorithm based on the minimization of the error signal variance to update thefilter coefficients,it has a certain delay,usually has a slow convergence speed,and the system response time is long and easily affected by the learning rate leading to the lack of system stability,which often fails to achieve the desired control effect in practice.In this paper,we propose an active control algorithm with near-est-neighbor trap structure and neural network feedback mechanism to reduce the coefficient update time of the FxLMS algorithm and use the neural network feedback mechanism to realize the parameter update,which is called NNR-BPFxLMS algorithm.In the paper,the schematic diagram of the feedback control is given,and the performance of the algorithm is analyzed.Under various noise conditions,it is shown by simulation and experiment that the NNR-BPFxLMS algorithm has the following three advantages:in terms of performance,it has higher noise reduction under the same number of sampling points,i.e.,it has faster convergence speed,and by computer simulation and sound pipe experiment,for simple ideal line spectrum noise,compared with the convergence speed of NNR-BPFxLMS is improved by more than 95%compared with FxLMS algorithm,and the convergence speed of real noise is also improved by more than 70%.In terms of stability,NNR-BPFxLMS is insensitive to step size changes.In terms of tracking performance,its algorithm responds quickly to sudden changes in the noise spectrum and can cope with the complex control requirements of sudden changes in the noise spectrum.

A New Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems

In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wolfe line search conditions.Numerical results show that the new method is efficient and stationary by comparing with PRP＋ method,so it can be widely used in scientific computation.

A Non-Monotone Trust Region Method with Non-Monotone Wolfe-Type Line Search Strategy for Unconstrained Optimization

In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.