Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonicity condition will decrease the convergence speed of this method. Therefore, improving and increasing the efficiency of this method is one of the most important issues and the attention of researchers.Methodology: Establishing a new adaptive trust region radius as well as combining the trust region method with a non-monotone strategy to avoid the adverse effects of monotonocity.Findings: A new adaptive trust region radius converged to zero is provided, and then a trust region combination is performed using a non-monotone strategy. Running the algorithm on a set of test functions shows that the new adaptive radius, along with the non-monotone strategy used, significantly improves the efficiency of the trust region method.Originality/Value: The presented non-monotone adaptive algorithm has a second-order convergence rate. In addition, it significantly reduces computational costs compared to traditional algorithms. On the other hand, the new adaptive radius avoids the ineffectiveness of the trust region close to the solution.

A bridge vibration measurement method by Unmanned Aerial Vehicles (UAVs) based on a Convolutional Neural Network (CNN) and Bayesian Optimization (BO) is proposed. In the proposed method, the video of the bridge structure is collected by a UAV, then the reference points in the background of the bridge and the target points on the bridge in the video are tracked by the Kanade-Lucas-Tomasi (KLT) optical flow method, so that their coordinates can be obtained. The BO is used to find the optimal hyper-parameter combination of a CNN, and the CNN based on BO is used to correct the bridge displacement signal collected by the UAV. Finally, the natural frequency of the bridge is extracted by processing the corrected displacement signals with Operational Modal Analysis (OMA). Moreover, a steel truss is used as the experimental model. The number of reference points and the shooting time of the UAV with the optimal correction effect of the BO-based CNN are obtained by two groups of comparative experiments, and the influence of the distance between structure and reference points on the correction effect of the BO-based CNN is determined by another group of comparative experiment. The static reference points are not required for the proposed method, which evidently enhances the applicability of UAVs; the conclusion of this paper has great guiding significance for the actual bridge vibration measurement.

While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems.‎ ‎Newton's method‎, ‎a notable numerical technique within the category of line search algorithms, is widely used for function optimization‎. The search direction and step length play crucial roles in this algorithm. ‎This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process‎. ‎Additionally‎, ‎numerical examples are provided to compare the effectiveness of this new method with another approach‎.

We make some ecient modications on the modied secant equation proposed by Zhangand Xu (2001). Then we introduce modied BFGS method using propose secant equation, and obtain some attractive results in theory and practice. We establish the global con-vergence property of the proposed method without convexity assumption on the objectivefunction. Numerical results on some testing problems from CUTEr collection show the pri-ority of the proposed method to some existing modied secant methods in practice.

The conjugate gradient ({CG}) method is one of the simplest and most widely used approaches for unconstrained optimization, and our focus is on two-dimensional problems with numerous practical applications. We devise three hybrid {CG} methods in which the hybrid parameter is constructed from the Barzilai–Borwein process, and in these hybrids, the weaknesses of each constituent method are mitigated by the strengths of the others. The conjugate gradient parameter is formed as a linear combination of two well-known CG parameters, blended by a scalar, enabling our new methods to solve the targeted problems efficiently. Under mild assumptions, we establish the descent property of the generated directions and prove the global convergence of the hybrid schemes. Numerical experiments on ten practical examples indicate that the proposed hybrid {CG} methods outperform standard {CG} methods for two-dimensional unconstrained optimization.

In this paper, we have investigated a new spectral Quasi-Newton (QN) algorithm. New search directions of the proposed algorithm increase its stability and increase the arrival to the optimum solution with a lowest cost value and our numerical applications on the standard Firefly Algorithm (FA)and the new proposed algorithm are powerful as in meta-heuristic field. Our new proposed algorithm has quite common uses in several sciences and engineering problems. Finally, our numerical results show that the proposed technique is the best and its accuracy higher than the accuracy of the standard FA. These numerical results are compared using statistical analysis to evaluate the efficiency and the robustness of new proposed algorithm.

In this paper, an efficient conjugate gradient method for unconstrained optimization is introduced. Parameters of the method are obtained by solving an optimization problem, and using a variant of the modified secant condition. The new conjugate gradient parameter benefits from function information as well as gradient information in each iteration. The proposed method has global convergence under mild assumptions. Using a collection of CUTEr problems, the method is compared with some existing algorithms to show its effectiveness.

The overall performance of a linear model predictive controller depends on proper adjustment of several design parameters. Most of these parameters have interdependent effects, which make their trial and error based tuning procedure very difficult. A systematic approach to overcome this problem is to reduce the number of adjustable parameters. This reduction is usually performed on the basis of sensitivity analysis, stability considerations or other objectives and constraints. The most reliable parameter, which can be independently tuned for performance improvement, is the control move suppression coefficient, l. In this paper, some tuning rules for adjusting this parameter, on the basis of specific performance criteria, are introduced. These rules are obtained from numerical analysis of the controller performance and are, therefore, applicable regardless of the existence of an approximated first-order model. The capabilities of the rules are demonstrated using simulations of regular and adaptive Dynamic Matrix Controllers (DMCs).

Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper, we propose a modified regularized Newton method for minimizing nonconvex functions whose Hessian matrix may be singular without line search. The proposed method is proved to converge globally if the Gradient and Hessian of the objective function are Lipschitz continuous. Moreover, we report numerical results that show that the proposed algorithm is competitive with the existing methods.