A nonmonotone conic trust region method based on line search for solving unconstrained optimization

In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods.     

A new modified nonmonotone adaptive trust region method for unconstrained optimization

In this paper, we present an adaptive trust region method for solving unconstrained optimization problems which combines nonmonotone technique with a new update rule for the trust region radius. At each iteration, our method can adjust the trust region radius of related subproblem. We construct a new ratio to adjust the next trust region radius which is different from the ratio in the traditional trust region methods. The global and superlinear convergence results of the method are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems.     

Combining nonmonotone conic trust region and line search techniques for unconstrained optimization

In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems.     

A new nonmonotone line search technique for unconstrained optimization

In this paper, we propose a new nonmonotone line search technique for unconstrained optimization problems. By using this new technique, we establish the global convergence under conditions weaker than those of the existed nonmonotone line search techniques.     

Adaptive nonmonotone line search method for unconstrained optimization

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.      

A truncated Newton method with nonmonotone line search for unconstrained optimization

In this paper, an unconstrained minimization algorithm is defined in which a nonmonotone line search technique is employed in association with a truncated Newton algorithm. Numerical results obtained for a set of standard test problems are reported which indicate that the proposed algorithm is highly effective in the solution of illconditioned as well as of large dimensional problems.     

An inexact line search approach using modified nonmonotone strategy for unconstrained optimization

This paper concerns with a new nonmonotone strategy and its application to the line search approach for unconstrained optimization. It has been believed that nonmonotone techniques can improve the possibility of finding the global optimum and increase the convergence rate of the algorithms. We first introduce a new nonmonotone strategy which includes a convex combination of the maximum function value of some preceding successful iterates and the current function value. We then incorporate the proposed nonmonotone strategy into an inexact Armijo-type line search approach to construct a more relaxed line search procedure. The global convergence to first-order stationary points is subsequently proved and the R-linear convergence rate are established under suitable assumptions. Preliminary numerical results finally show the efficiency and the robustness of the proposed approach for solving unconstrained nonlinear optimization problems.     

A nonmonotone trust-region line search method for large-scale unconstrained optimization

We consider an efficient trust-region framework which employs a new nonmonotone line search technique for unconstrained optimization problems. Unlike the traditional nonmonotone trust-region method, our proposed algorithm avoids resolving the subproblem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed approach for solving unconstrained optimization problems.     

A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization

A new subspace minimization conjugate gradient algorithm with a nonmonotone Wolfe line search is proposed and analyzed. In the scheme, we propose two choices of the search direction by minimizing a quadratic approximation of the objective function in special subspaces, and state criterions on how to choose the direction. Under given conditions, we obtain the significant conclusion that each choice of the direction satisfies the sufficient descent property. Based on the idea on how the function is close to a quadratic function, a new strategy for choosing the initial stepsize is presented for the line search. With the used nonmonotone Wolfe line search, we prove the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising.     

A new trust region method for unconstrained optimization

In this paper, we propose a new trust region method for unconstrained optimization problems. The new trust region method can automatically adjust the trust region radius of related subproblems at each iteration and has strong global convergence under some mild conditions. We also analyze the global linear convergence, local superlinear and quadratic convergence rate of the new method. Numerical results show that the new trust region method is available and efficient in practical computation.     

A nonmonotone adaptive trust region method for unconstrained optimization based on conic model

In this paper, we present a nonmonotone adaptive trust region method for unconstrained optimization based on conic model. The new method combines nonmonotone technique and a new way to determine trust region radius at each iteration. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments show that our algorithm is effective.     

A new trust region dogleg method for unconstrained optimization

Abstract. This paper presents a new trust region dogleg method for unconstrained optimization.The method can deal with the case when the Hessian B of quadratic models is indefinite. It isproved that the method is globally convergent and has a quadratic convergence rate if Under certain conditions, the solution obtained by the method is even a second order     

A class of nonmonotone trust region algorithms for unconstrained optimization problems

A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q-quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed. Project supported by the National Natural Science Foundation of China (Grant No. 19136012).     

An unconstrained optimization method using nonmonotone second order Goldstein's line search

In this paper,an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed.By using the negative curvature information from the Hessian, the sequence generated is shown to converge to a stationary point with the second order optimality conditions.Numerical tests on a set of standard test problems confirm the efficiency of our new method.     

A new non-monotone self-adaptive trust region method for unconstrained optimization

In this paper, based on a simple model of trust region sub-problem, we combine the trust region method with the non-monotone and self-adaptive techniques to propose a new non-monotone self-adaptive trust region algorithm for unconstrained optimization. By use of the simple model, the new method needs less memory capacitance, computational complexity and CPU time. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is effective and attractive for large-scale optimization problems.     

An unconstrained optimization method using nonmonotone second order Goldstein’s line search

In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein’s line search is proposed. By using the negative curvature information from the Hessian, the sequence generated is shown to converge to a stationary point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency of our new method. This work was supported by the National Natural Science Foundation of China (Grant No. 10231060) and the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No. 20040319003)     

A nonmonotone filter trust region method for nonlinear constrained optimization

In this paper, we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. Similar to Bryd–Omojokun class of algorithms, each step is composed of a quasi-normal step and a tangential step. This new method has more flexibility for the acceptance of the trial step compared to the filter methods, and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the globally convergence properties. Numerical tests are presented that confirm the efficiency of the approach.     

Two accelerated nonmonotone adaptive trust region line search methods

Hybridizing monotone and nonmonotone approaches, we employ a modified trust region ratio in which more information is provided about the agreement between the exact and the approximate models. Also, we use an adaptive trust region radius as well as two accelerated Armijo-type line search strategies to avoid resolving the trust region subproblem whenever a trial step is rejected. We show that the proposed algorithm is globally and locally superlinearly convergent. Comparative numerical experiments show practical efficiency of the proposed accelerated adaptive trust region algorithm.     

An improved trust region method for unconstrained optimization

In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust region centered at the current iteration point,but within an improved one centered at some point located in the direction of the negative gradient,while the current iteration point is on the boundary set.We prove the global convergence properties of the new improved trust region algorithm and give the computational results which demonstrate the effectiveness of our algorithm.