An Active-Set Projected Trust Region Algorithm for Box Constrained Optimization Problems

An active-set projected trust region algorithm is proposed for box constrained optimization problems, where the given algorithm is designed by three steps. First, the projected gradient direction which normally has better numerical performance is introduced. Second, the projected trust region direction that often possesses good convergence is defined, where the matrix of trust region subproblem is updated by limited memory strategy. Third, in order to get both good numerical performance and convergence, the authors define the final search which is the convex combination of the projected gradient direction and the projected trust region direction. Under suitable conditions, the global convergence of the given algorithm is established. Numerical results show that the presented method is competitive to other similar methods.

A Dynamic Active-Set Method for Linear Programming

An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.

Numerical Computational Heuristic Through Morlet Wavelet Neural Network for Solving the Dynamics of Nonlinear SITR COVID-19

The present investigations are associated with designing Morlet wavelet neural network(MWNN)for solving a class of susceptible,infected,treatment and recovered(SITR)fractal systems of COVID-19 propagation and control.The structure of an error function is accessible using the SITR differential form and its initial conditions.The optimization is performed using the MWNN together with the global as well as local search heuristics of genetic algorithm(GA)and active-set algorithm(ASA),i.e.,MWNN-GA-ASA.The detail of each class of the SITR nonlinear COVID-19 system is also discussed.The obtained outcomes of the SITR system are compared with the Runge-Kutta results to check the perfection of the designed method.The statistical analysis is performed using different measures for 30 independent runs as well as 15 variables to authenticate the consistency of the proposed method.The plots of the absolute error,convergence analysis,histogram,performancemeasures,and boxplots are also provided to find the exactness,dependability and stability of the MWNN-GA-ASA.

Numerical Solutions of a Novel Designed Prevention Class in the HIV Nonlinear Model

The presented research aims to design a new prevention class(P)in the HIV nonlinear system,i.e.,the HIPV model.Then numerical treatment of the newly formulated HIPV model is portrayed handled by using the strength of stochastic procedure based numerical computing schemes exploiting the artificial neural networks(ANNs)modeling legacy together with the optimization competence of the hybrid of global and local search schemes via genetic algorithms(GAs)and active-set approach(ASA),i.e.,GA-ASA.The optimization performances through GA-ASA are accessed by presenting an error-based fitness function designed for all the classes of the HIPV model and its corresponding initial conditions represented with nonlinear systems of ODEs.To check the exactness of the proposed stochastic scheme,the comparison of the obtained results and Adams numerical results is performed.For the convergence measures,the learning curves are presented based on the different contact rate values.Moreover,the statistical performances through different operators indicate the stability and reliability of the proposed stochastic scheme to solve the novel designed HIPV model.

Swarming Computational Approach for the Heartbeat Van Der Pol Nonlinear System

The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model(VP-HBM)using the feedforward artificial neural networks(ANNs)under the optimization of particle swarm optimization(PSO)hybridized with the active-set algorithm(ASA),i.e.,ANNs-PSO-ASA.The global search PSO scheme and local refinement of ASA are used as an optimization procedure in this study.An error-based merit function is defined using the differential VP-HBM form as well as the initial conditions.The optimization of the merit function is accomplished using the hybrid computing performances of PSO-ASA.The designed performance of ANNs-PSO-ASA is implemented for the numerical treatment of the VP-HBM dynamics by fluctuating the pulse shape adjustment terms,external forcing factor and damping coefficient with fixed ventricular contraction period.To perform the correctness of the present scheme,the obtained numerical results through the designed ANN-PSO-ASA will be compared with the Adams numerical method.The statistical investigations with larger dataset are provided using the“mean absolute deviation”,“Theil’s inequality coefficient”and“variance account for”operators to perform the applicability,reliability,and effectiveness of the designed ANNs-PSO-ASA scheme for solving the VP-HBM.

Constraint Optimal Selection Techniques (COSTs) for Linear Programming

We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add multiple constraints. We give an interpretation of the new COST’s selection rule, which considers both the depth of constraints as well as their angles from the objective function. We provide computational comparisons of the COST with existing linear programming algorithms, including other COSTs in the literature, for some large-scale problems. Finally, we discuss conclusions and future research.

A TRUST-REGION ALGORITHM FOR SOLVING MINI-MAX PROBLEM

In this paper, we propose an algorithm for solving inequality constrained mini-max optimization problem. In this algorithm, an active set strategy is used together with mul- tiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem. A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. A global convergence analysis for the proposed algorithm is presented under some conditions. To show the efficiency of the algorithm numerical results for a number of test problems are reported.