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This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newton formulas helps to handle large-scale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a fi rst-order stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving large-scale unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

State transition algorithm (STA) is an efficient and powerful metaheuristic method for solving global optimization problems, and it has been successfully applied in many engineering fields in the past few years. However, the basic STA has weak local search capability and shows slow convergence rate and low convergence accuracy in the later search stage. In view of the above shortcomings, an adaptive state transition algorithm (ASTA) with local enhancement is proposed in this paper. Firstly, the order of using state transformation operators and the optimal parameters of the operators are considered in each iteration of ASTA, and a statistical method is employed to adaptively select the optimal transformation operator and the parameter values of the optimal operator to speed up the search process. Then, an adaptive call strategy is adopted to determine its convergence to the neighborhood of the optimal solution and to decide whether to perform the quasi-Newton operator for local enhancement. Finally, the degree to which the current solution is close to the optimal solution is judged by the information of historical solutions, and an analytical solution is quickly obtained by calling the quadratic interpolation operator. The effectiveness of the proposed ASTA is checked, through a comparison with other metaheuristic methods, on 15 benchmark functions and several real-world optimization problems. Experimental results show that ASTA has a stronger search capability than the basic STA, STA variants, and some state-of-the-art metaheuristic methods. • An adaptive state transition algorithm is proposed. • Local enhancement techniques are employed to speed up the search efficiency. • The proposed algorithm is verified on some practical engineering problems. [ABSTRACT FROM AUTHOR]