Model guided extremum seeking control of electromagnetic micromirrors

In this paper, a simplified dynamic model is constructed to describe the main characteristic of electromagnetic micro-mirror. Then, based on the information provided by the derived simplified model, a model-guided extremum seeking control (MGESC) scheme with backtracking line search is developed, which can automatically estimate the best value of step-size at each search iteration to improve the performance of the control system for target tracking. Then, the convergence of the proposed MGES algorithm is proved. Finally, the experimental results and the simulations are presented to verify the proposed method.

An Advanced Extremum Seeking Scheme for the Target Trajectory in Electromagnetic Micromirror System

Now two problems result in bad control in the development of the electromagnetic micromirror system. One is that theoretical model in electromagnetic micromirror system is difficult to be determined; Another is that parameters in common control need to be tuned according to the experience. In this paper, cost function concept is proposed to determine the model order in slow-scan axis control of the electromagnetic micromirror. Then recursive least square scheme is built to off-line identify this model. Furthermore, an advanced extremum seeking scheme along with backtracking line search is exploited, which can automatically identify the best parameter value before each extremum search to improve the controllability based on this model for the target trajectory in slow-scan axis control. And the convergence of it is proved. Finally, the experiments and the simulations verify this method proposed valid.

MULTIPLE USE OF BACKTRACKING LINE SEARCH IN UNCONSTRAINED OPTIMIZATION

The gradient method is a very efficient iterative technique for solving unconstrained optimization problems. Motivated by recent modifications of some variants of the SM method, this study proposed two methods that are globally convergent as well as computationally efficient. Each of the methods is globally convergent under the influence of a backtracking line search. Results obtained from the numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods.

A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

A new rule for calculating the parameter t involved in each iteration of the MHSDL (Dai-Liao) conjugate gradient (CG) method is presented. The new value of the parameter initiates a more efficient and robust variant of the Dai-Liao algorithm. Under proper conditions, theoretical analysis reveals that the proposed method in conjunction with backtracking line search is of global convergence. Numerical experiments are also presented, which confirm the influence of the new value of the parameter t on the behavior of the underlying CG optimization method. Numerical comparisons and the analysis of obtained results considering Dolan and Moré’s performance profile show better performances of the novel method with respect to all three analyzed characteristics: number of iterative steps, number of function evaluations, and CPU time.

SVD++ Recommendation Algorithm Based on Backtracking

Collaborative filtering (CF) has successfully achieved application in personalized recommendation systems. The singular value decomposition (SVD)++ algorithm is employed as an optimized SVD algorithm to enhance the accuracy of prediction by generating implicit feedback. However, the SVD++ algorithm is limited primarily by its low efficiency of calculation in the recommendation. To address this limitation of the algorithm, this study proposes a novel method to accelerate the computation of the SVD++ algorithm, which can help achieve more accurate recommendation results. The core of the proposed method is to conduct a backtracking line search in the SVD++ algorithm, optimize the recommendation algorithm, and find the optimal solution via the backtracking line search on the local gradient of the objective function. The algorithm is compared with the conventional CF algorithm in the FilmTrust, MovieLens 1 M and 10 M public datasets. The effectiveness of the proposed method is demonstrated by comparing the root mean square error, absolute mean error and recall rate simulation results.

Quasi-solution of linear inverse problems in non-reflexive Banach spaces

We consider the method of quasi-solutions (also referred to as Ivanov regularization) for the regularization of linear ill-posed problems in non-reflexive Banach spaces. Using the equivalence to a metric projection onto the image of the forward operator, it is possible to show regularization properties and to characterize parameter choice rules that lead to a convergent regularization method, which includes the Morozov discrepancy principle. Convergence rates in a suitably chosen Bregman distance can be obtained as well. We also address the numerical computation of quasi-solutions to inverse source problems for partial differential equations in {L^{\infty}(\Omega)} using a semi-smooth Newton method and a backtracking line search for the parameter choice according to the discrepancy principle. Numerical examples illustrate the behavior of quasi-solutions in this setting.

Parameter Estimation of Spring-Damping System using Unconstrained Optimization by the Quasi-Newton Methods using Line Search Techniques

Optimization is the basic tools to study the behaviour of many complicated mechanical systems by having the knowledge of differential equations which determine the system. The basis of this paper was to present a method to estimate the parameters such as spring constant and damping coefficient of the spring damped system by unconstrained optimization using derivative methods Such as quasi-newton method by Broyden-Fletcher-Goldfarb-Shanno and davidon-Fletcher-Powell hessian updating method by using backtracking line search methods along with Armijo’s condition.it uses the output error approximation procedure. It shows the convergence of different methods which are used to estimate the parameters and how accurately they are measured.

INITIAL IMPROVEMENT OF THE HYBRID ACCELERATED GRADIENT DESCENT PROCESS

We improve the convergence properties of the iterative scheme for solving unconstrained optimisation problems introduced in Petrovic et al. [‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi:10.1007/s11075-017-0460-4] by optimising the value of the initial step length parameter in the backtracking line search procedure. We prove the validity of the algorithm and illustrate its advantages by numerical experiments and comparisons.

SSEalign: accurate function prediction of bacterial unannotated protein, based on effective training dataset

The functions of numerous bacterial proteins remain unknown because of the variety of their sequences. The performances of existing prediction methods are highly weak toward these proteins, leading to the annotation of “hypothetical protein” deposited in NCBI database. Elucidating the functions of these unannotated proteins is an urgent task in computational biology. We report a method about secondary structure element alignment called SSEalign based on an effective training dataset extracting from 20 well-studied bacterial genomes. The experimentally validated same genes in different species were selected as training positives, while different genes in different species were selected as training negatives. Moreover, SSEalign used a set of well-defined basic alignment elements with the backtracking line search algorithm to derive the best parameters for accurate prediction. Experimental results showed that SSEalign achieved 91.2% test accuracy, better than existing prediction methods. SSEalign was subsequently applied to identify the functions of those unannotated proteins in the latest published minimal bacteria genome JCVI-syn3.0. Results indicated that At least 99 proteins out of 149 unannotated proteins in the JCVI-syn3.0 genome could be annotated by SSEalign. In conclusion, our method is effective for the identification of protein homology and the annotation of uncharacterized proteins in the genome.