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We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from the CUTEst package. [ABSTRACT FROM AUTHOR]

In this paper, a trust-region procedure is proposed for the solution of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the required number subproblems that must be solved. The global convergence and the local Q-quadratic convergence rate of the proposed approach are proved. Preliminary numerical results of the proposed algorithm are also reported which indicate the promising behavior of the new procedure for solving the nonlinear system. [ABSTRACT FROM AUTHOR]

Existing principal curve algorithms have some drawbacks such as time consuming and narrow application scope in practice, since these algorithms are mainly based on global optimization. In this paper, we present the concept of Constraint Local Principal Curve (CLPC), which uses local optimization methods and restricts the principal curve with two fixed endpoints to reduce the computational complexity. In addition, we propose three CLPC algorithms by Local Optimization and Adaptive Radius to expand the range of applications and increase the solution quality. The first algorithm, i.e., CLPCg is based on greedy thinking. The second algorithm, i.e., CLPCs uses one dimensional search and the last algorithm CLPCc combines the greedy thinking and one dimensional search. Then, we define six performance indices to evaluate the performance of the CLPC algorithms. Finally, we present some numerical experiments with three simulation data sets and two GPS measured data sets in both highway and railway. The results indicate that all of the three CLPC algorithms can obtain high-accuracy data from multiple low-accuracy data efficiently. The CLPC algorithms can improve the accuracy and computational speed compared with the existing K-segment principal curve (KPC) algorithm. In addition, CLPCc outperforms CLPCg and CLPCs according to the comprehensive experiments while CLPCg runs much faster than other ones. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new adaptive trust-region approach to solve systems of nonlinear equations. In order to improve the efficiency of adaptive radius strategy proposed by Esmaeili and Kimiaei [8], Barzilai Borwein technique (BB) [3] with low memory is used which can truly control the trust-region radius. In addition, the global convergence of the new approach is proved. Computational experience suggests that the new approach is more effective in practice in comparison with other adaptive trust-region algorithms.

This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems.

As the pixel information of depth image is derived from the distance information, when implementing SURF algorithm with KINECT sensor for static sign language recognition, there can be some mismatched pairs in palm area. This paper proposes a feature point selection algorithm, by filtering the SURF feature points step by step based on the number of feature points within adaptive radius r and the distance between the two points, it not only greatly improves the recognition rate, but also ensures the robustness under the environmental factors, such as skin color, illumination intensity, complex background, angle and scale changes. The experiment results show that the improved SURF algorithm can effectively improve the recognition rate, has a good robustness.