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.

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.

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).

In this paper, we present a nonmonotone trust-region algorithm for UNCONSTRAINED optimization. We first introduce a variant of the nonmonotone strategy proposed by Ahookhosh & Amini [1] and incorporate it into the trust-region framework to construct a more efficient approach. Our new nonmonotone strategy combines the current function value with the maximum function values in some prior successful iterates. For iterates far away from the optimizer, we give a very strong nonmonotone strategy. In the vicinity of the optimizer, we have a weaker nonmonotone strategy. It leads to a medium nonmonotone strategy when iterates are not far away from or close to the optimizer. Theoretical analysis indicates that the new approach converges globally to a first-order critical point under classical assumptions. In addition, the local convergence is studied. Extensive numerical experiments for UNCONSTRAINED optimization problems are reported showing that the new algorithm is robust and efficient.

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.