Nonmonotone Trust Region Algorithm Research Articles

A new nonmonotone adaptive trust region method based on simple quadratic models

Based on simple quadratic models of the trust region subproblem, we combine the trust region method with the nonmonotone and adaptive techniques to propose a new nonmonotone adaptive trust region algorithm for unconstrained optimization. Unlike traditional trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function’s Hessian. The new method needs less memory capacitance and computational complexity. 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 unconstrained problems.

COMBINATION ADAPTIVE TRUST REGION METHOD BY NON-MONOTONE STRATEGY FOR UNCONSTRAINED NONLINEAR PROGRAMMING

In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function evaluations. The new algorithm preserves the global convergence and has local superlinear and quadratic convergence under suitable conditions. Numerical experiments exhibit that the new trust region algorithm is very efficient and robust for unconstrained optimization problems.

A Non-Monotone Trust Region Algorithm with Memory Model for Unconstrained Optimization

A Non-Monotone Trust Region Algorithm with Memory Model for Unconstrained Optimization

A Mixed Algorithm for Nonlinear Complementarity Problems

Combining nonmonotone trust region algorithms and PSO methods, we propose a mixed method for nonlinear complementarity problems. The iterative formula of μ k is very simple. When the determinant of B k +λ k I is very large or small, the PSO method will obtain a new point which gets us better astringency. Numerical test results show the effectiveness of this algorithm.

Nonmonotone trust region algorithm for unconstrained optimization problems

In this paper, a nonmonotone trust region algorithm for unconstrained optimization problems is presented. In the algorithm, a kind of nonmonotone technique, which is evidently different from Grippo, Lampariello and Lucidi’s approach, is used. Under mild conditions, global and local convergence results of the algorithm are established. Preliminary numerical results show that the new algorithm is efficient.

Global Convergence of a Nonmonotone Trust Region Algorithm with Memory for Unconstrained Optimization

In this paper, we consider a trust region algorithm for unconstrained optimization problems. Unlike the traditional memoryless trust region methods, our trust region model includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. The numerical tests are also given to show the efficiency of our proposed method.

A nonmonotone adaptive trust-region algorithm for symmetric nonlinear equations

In this paper, we propose a nonmonotone adap-tive trust-region method for solving symmetric nonlinear equations problems. The convergent result of the presented method will be estab-lished under favorable conditions. Numerical results are reported.

A new hybrid method for nonlinear complementarity problems

In this paper, a new hybrid method is proposed for solving nonlinear complementarity problems (NCP) with P 0 function. In the new method, we combine a smoothing nonmonotone trust region method based on a conic model and line search techniques. We reformulate the NCP as a system of semismooth equations using the Fischer-Burmeister function. Using Kanzow's smooth approximation function to construct the smooth operator, we propose a smoothing nonmonotone trust region algorithm of a conic model for solving the NCP with P 0 functions. This is different from the classical trust region methods, in that when a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength is defined by a line search. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, the superlinear convergence of the algorithm is established without a strict complementarity condition.

Global and local convergence of a nonmonotone trust region algorithm for equality constrained optimization

This paper presents a nonmonotone trust region algorithm for equality constrained optimization problems. Under certain conditions, we obtain not only the global convergence in the sense that every limit point is a stationary point but also the one step superlinear convergence rate. Numerical tests are also given to show the efficiency of the proposed algorithm.

A nonmonotone quasi-Newton trust-region method of conic model for unconstrained optimization

This paper presents a new nonmonotone quasi-Newton trust-region algorithm of the conic model for the solution of unconstrained optimization problems, where the computation of the horizontal vectors is easier and the approximate Hessian matrices can be maintained positive definite. Under reasonable assumptions, the global convergence, the locally linear and superlinear convergence of the proposed algorithm are developed, respectively. It is well known that in applying trust-region algorithms, the basic issue is how to solve the trust-region subproblem efficiently. To deal with the issue, an approximate solution method is developed in this paper. Note that the approximate solution method not only is computationally cheap, but also preserves the strong convergence properties as the exact solution methods. Numerical results are shown for a number of test problems from the literature.

Numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters

In this paper, a numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters is presented. We compare the numerical efficiency of two classes of nonmonotone trust region (NTR) algorithms in the context of unconstrained optimization. We examine the sensitivity of the algorithms to the parameters related to the nonmonotone technique and the initial trust region radius. We show that the numerical efficiency of nonmonotone trust region algorithms can be improved by choosing appropriate parameters. Based on extensive numerical tests, some efficient ranges of these parameters for nonmonotone trust region algorithms are recommended.

Nonmonotone Trust-Region Method for Nonlinear Programming with General Constraints and Simple Bounds

In this paper, we propose a nonmonotone trust-region algorithm for the solution of optimization problems with general nonlinear equality constraints and simple bounds. Under a constant rank assumption on the gradients of the active constraints, we analyze the global convergence of the proposed algorithm.

A nonmonotone trust-region algorithm with nonmonotone penalty parameters for constrained optimization

In this paper, we present a nonmonotone trust-region algorithm with nonmonotone penalty parameters for the solution of optimization problems, with nonlinear equality constraints and bound constraints. The proposed algorithm combines an SQP approach with a trust-region strategy to globalize the process. Each step is obtained through the computation of a normal step (to reduce infeasibility) and a tangential step (to decrease some merit function). The algorithm makes use of an augmented Lagrangian function as merit function, and allows the value of this merit function and the penalty parameter involved in it to decrease nonmonotonically. The global convergence theory for the proposed algorithm is developed without regularity assumption, and shows that any limit point of the sequence generated by the algorithm is a ϕ-stationary point, while at least one limit point, under the suitable assumptions, is a substationary point (and a stationary point if it is feasible). Some preliminary numerical experiments are also reported.

A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints

In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient.

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.

Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints

This paper presents two new trust-region methods for solving nonlinear optimization problems over convex feasible domains. These methods are distinguished by the fact that they do not enforce strict monotonicity of the objective function values at successive iterates. The algorithms are proved to be convergent to critical points of the problem from any starting point. Extensive numerical experiments show that this approach is competitive with the LANCELOT package.

Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints

Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints