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In this paper, we propose the use of a surrogate model based on mixtures of liner Taylor polynomials for Trust Region methods. The main objective of this model is to reduce the myopia presented in surrogate models based on single low-order Taylor expansions by which, the number of iterations during the optimization process of Trust Region based methods can be increased. The proposed model is built as follows: points are sampled from the search space, at each sampled point a surrogate model of the cost function is built by using a linear Taylor polynomial and then, cost functions can be locally approximated via a convex combination of such surrogate models. The Trust Region framework is then utilized in order to validate the quality of the proposed model. Experimental tests are performed making use of the three-dimensional variational optimization problem from data assimilation with an atmospheric general circulation model. The results reveal that, the use of our proposed surrogate model can improve the quality of the local approximations and even more, their use can decrease the number of iterations needed in order to obtain accurate solutions. [ABSTRACT FROM AUTHOR]

From 1952 until now, the sufficient descent property and the global convergence of conjugate gradient (CG) methods have been studied extensively. However, the sufficient descent property and the global convergence of some CG methods such as the method of Polak, Ribière, and Polyak (PRP) and the method of Hestenes and Stiefel (HS) have not been established yet under the strong Wolfe line search. In this paper, based on Yousif (Yousif, 2020) we present a criterion that guarantees the generation of descent search directions property and the global convergence of CG methods when they are applied under the strong Wolfe line search. Moreover, the PRP and the HS methods are restricted in order to satisfy the presented criterion, so new modified versions of PRP and HS are proposed. Finally, to support the theoretical proofs, a numerical experiment is done. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods have played a vital role in finding the minimizers of large-scale unconstrained optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. Based on the Liu-Storey conjugate gradient method, in this paper, we present a Liu-Storey type method for finding the minimizers of large-scale unconstrained optimization problems. The direction of the proposed method is constructed in such a way that the sufficient descent condition is satisfied. Furthermore, we establish the global convergence result of the method under the standard Wolfe and Armijo-like line searches. Numerical findings indicate that our presented approach is efficient and robust in solving large-scale test problems. In addition, an application of the method is explored. [ABSTRACT FROM AUTHOR]

Abstract: According to the proposed particle swarm optimization (PSO) difference model in the paper, the state sequence of a single particle and swarm state sequence are defined first, and their Markov property are analyzed, after that, it is demonstrated that the set of optimal states are closed set. Moreover, the one-step transition probability of a particle is calculated. Considering the total probability formula and the Markov properties, the transition probability of the optimal set is deduced. According to the derived conclusion, the inertia weight ω and accelerate factor c of PSO are discussed. Finally, the premature convergence and divergent problem are explained, furthermore, it is proved that the standard PSO algorithm reaches the global optimum with certain probability. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a modified PRP conjugate gradient method which develops a new formula for parameter and possesses the following properties: (1)the sufficient descent property holds without any line searches; (2)this method inherits an important property of Polak-Ribière-Polyak(PRP) method;(3)under some assumable conditions, the method is globally convergent. Preliminary numerical results show that this method is very efficient. [Copyright &y& Elsevier]

Abstract: This paper, we discussed a class of nonconvex composite multi-objective optimization problems under the weaker assumption conditions. We construct a new homotopy continuation mapping and obtain a smooth bounded homotopy path which converges globally to the K-K-T solution of multi-objective programming. A numerical example was provided to exhibit the effectiveness of this method. [Copyright &y& Elsevier]

In this paper, a rank-one updated mehod for solving symmetric nonlinear equations is proposed. This method possesses some features: (1) The updated matrix is positive definite whatever line search technique is used; (2) The search direction is descent for the norm function; Under reasonable conditions, we establish its global convergence. Numerical results show that the presented method is competitive to the normal BFGS method for the test problems. [ABSTRACT FROM AUTHOR]

In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: (1) The updated matrix is positive definite whatever line search technique is used; (2) The search direction is descent for the norm function; Under reasonable conditions, we establish its global convergence. Numerical results show that the presented method is competitive to the normal BFGS method for the test problems. [ABSTRACT FROM AUTHOR]

In this paper, a new conjugate gradient formula βNewk is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with some line searches such as the exact line search, the Grippo-Lucidi line search and the Wolfe-Powell line search are discussed. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula βNewk ⩾ 0, and the search directions dk which are generated by the given βNewk under the strong Wolfe-Powell line search satisfy the sufficient descent condition. Preliminary numerical results show that the proposed methods are efficient. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that the search direction plays a main role in the line search method. In this paper, we propose a new search direction together with the Wolfe line search technique and one nonmonotone line search technique for solving unconstrained optimization problems. The given methods possess sufficiently descent property without carrying out any line search rule. The convergent results are established under suitable conditions. For numerical results, analysis of one probability shows that the new methods are more effective, robust, and stable, than other similar methods. Numerical results of two statistical problems also show that the presented methods are more interesting than other normal methods. [Copyright &y& Elsevier]

In this paper, a new multi-model direct adaptive decoupling controller is presented for multivariable processes, which includes multiple fixed optimal controllers, one free-running adaptive controller, and one re-initialized adaptive controller. The fixed controllers provide initial control to the process if its model lies in the corresponding region. For each controller selected, the re-initialized adaptive controller uses the values of this particular controller to improve the adaptation speed. This controller may replace the fixed controller at a later stage according to the switching criterion which is to select the best one among all controllers. A free-running adaptive controller is also added to guarantee the overall system stability. Different from the multiple models adaptive control structure proposed in Narendra, Balakrishnan, and Ciliz [Adaptation and learning using multiple models, switching, and tuning. IEEE Control Syst. Mag. 15, 37-51 (1995)], the method not only is applicable to the multi-input multi-output processes but also identifies the decoupling controller parameters directly, which reduces both the computational burden and the chances of a singular matrix during the process of determining controller parameters. Several examples for a wind tunnel process are given to demonstrate the effectiveness and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

• Novel SI algorithm namely Accelerated Grey Wolf Optimization (AGWO) which integrates mathematical model into GWO to eradicate the local confinement as well as to accelerate its global convergence speed. • AGWO holds diversity measure and parameter tuned strategy to balance intensification and diversification process. Grey Wolf Optimizer (GWO) belongs to the family of swarm intelligence and population-based algorithm which mimics the social behaviors of gray wolf packs. Due to its ease and viability, various researchers from different domains applied GWO to solve their research problems. However, GWO ought to have solid yet adjusted strengthening and broadening procedure to upgrade its execution. This paper introduces a novel SI algorithm, namely Accelerated gray Wolf Optimization (AGWO) which incorporates the enhanced hierarchy into GWO technique. Firstly, we introduce a mathematical model to strengthen the local and global search process. Then, we propose a diversity measure to eradicate the local confinement and to keep perfect balance between intensification and diversification process. Further, parameter tuned strategy is incorporated to speed up the convergence rate. The proposed methodology is experimented using MATLAB and tested with twenty-three mathematical benchmark problems (such as unimodal, multimodal and fixed dimensional multimodal functions). The search capability of the AGWO is compared with the generic GWO and various state-of-art swarm intelligence algorithms. Empirical results expose that AGWO provides better performance as per the standard deviation, best value and convergence curve compared to other algorithms. The sensitivity study of the proposed AGWO algorithm provides better results for 19 benchmark functions out of 23 benchmark functions in terms of minimal computation time and better convergence rate. [ABSTRACT FROM AUTHOR]