强Wolfe-Powell线搜索下共轭梯度法的全局收敛性

给出一类求解非线性无约束优化问题的共轭梯度新算法。在强Wolfe-Powell线搜索下所给公式具有充分下降性,所给该新算法具有全局收敛性。

修正的强Wolfe-Powell线搜索下的PRP方法的全局收敛性(英文)

众所周知,原始的PRP方法是不全局收敛的.本文提出一个修正的强Wolfe-Powell线搜索.在这个新的线搜索下,如果每个搜索方向都是下降的,那么可以得到PRP方法的全局收敛性.而且,我们的初始数值结果表明这个新的PRP方法与原始的PRP方法相当,甚至比它稍好一些.

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.

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.

工程优化计算中Wolfe-Powell准则的研究

讨论在工程优化计算的线搜索阶段如何寻找满足Wolfe Powell准则的步长问题 .针对插值法使用的技巧与方法 ,给出了一个改进的高效稳定的算法 .然后通过数值实验表明 ,与精确线搜索相比 ,采用Wolfe Pow ell准则的非精确线搜索不仅能大大提高优化算法的效率 ,而且还增强了算法的数值稳定性 。

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.

An Improved Line Search and Trust Region Algorithm

In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.

ALGORITHM AND IMPLEMENTATION OF AUTO-SEARCHING WELD LINE FOR WELDING MOBILE ROBOT

An algorithm of auto-searching weld line for welding mobile robot is presented. Auto-searching weld line is that the robot can automatically recognize a weld groove according to the characteristics of the weld groove before welding, and then adjust itself posture to the desired status preparing for welding, namely, it is a process that the robot autonomously aligns itself to the center of welding seam. Firstly, the configuration of welding mobile robot with the function of auto-searching weld line is introduced, then the algorithm and implementation of auto-searching weld line are presented on the basis of kinematics model of the robot, at last trajectory planning among auto-searching weld line is investigated in detail. The experiment result shows that the developed welding mobile robot can successfully implement the task of auto-searching weld line before welding, tracking error precision can be controlled to approximate ±1.5 mm, and satisfy the requirement of practical welding project.

Wolfe-Powell下的记忆梯度算法

提出了一种记忆梯度法的主要参数d_k的新形式,分析了该算法在Wplfe-Powell搜索下的全局收敛性,适合解决大型优化问题。

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.

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 Solution of the Eigenvalue Complementarity Problem by a Line Search Filter-SQP Algorithm

In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.

Relay Beamforming Design for Physical Layer Secure Communication via Line Search Algorithm

This paper considers a physical layer se-curity model in wireless communications.Two legit-imate users communicate through several relays with the presence of an eavesdropper.We jointly design the relay beamforming weights and minimize the to-tal relay transmit power,while ensuring users’Qual-ity of Services and preventing the information being eavesdropped at the same time.The problem is a robust optimization problem,because of the imper-fect channel state information from users and relays to the eavesdropper.First the original problem is sim-plified,where the high order robust terms are omit-ted.Then we design an iterative algorithm based on line search,by solving two Quadratically Con-strained Quadratic Programming subproblems and a one-dimensional subproblem.Simulation results indi-cate that the proposed algorithm outperforms the state of the arts.

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.

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.

A Nonmonotone Line Search Method for Symmetric Nonlinear Equations

In this paper, we propose a new method which based on the nonmonotone line search technique for solving symmetric nonlinear equations. The method can ensure that the search direction is descent for the norm function. Under suitable conditions, the global convergence of the method is proved. Numerical results show that the presented method is practicable for the test problems.

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.

Optimization of Energy Resource Management for Assembly Line Balancing Using Adaptive Current Search

This paper aimed to present the optimization of energy resource management in a car factory by the adaptive current search (ACS)—one of the most efficient metaheuristic optimization search techniques. Assembly lines of a specific car factory considered as a case study are balanced by the ACS to optimize their energy resource management. The workload variance of the line is performed as the objective function to be minimized in order to increase the productivity. In this work, the ACS is used to address the number of tasks assigned for each workstation, while the sequence of tasks is assigned by factory. Three real-world assembly line balancing (ALB) problems from a specific car factory are tested. Results obtained by the ACS are compared with those obtained by the genetic algorithm (GA), tabu search (TS) and current search (CS). As results, the ACS outperforms other algorithms. By using the ACS, the productivity can be increased and the energy consumption of the lines can be decreased significantly.

A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search

In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.