An Affine Scaling Interior Trust-Region Algorithm Combining Backtracking Line Search with Filter Technique for Nonlinear Constrained Optimization

Motivated by the method of Su and Pu (2009), we present an improved nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. In our algorithm a modified nonmonotone filter technique is proposed and the restoration phase is not needed. At every iteration, in common with the composite-step SQP methods, the step is viewed as the sum of two distinct components, a quasinormal step and a tangential step. A more relaxed accepted condition for trial step is given and a crucial criterion is weakened. Under some suitable conditions, the global convergence is established. In the end, numerical results show our method is effective.

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Nonmonotone conic trust region method with line search technique for bound constrained optimization

RAIRO - Operations Research ◽

10.1051/ro/2017054 ◽

2019 ◽

Vol 53 (3) ◽

pp. 787-805

Author(s):

Lijuan Zhao

Keyword(s):

Constrained Optimization ◽

Line Search ◽

Optimization Problems ◽

Trust Region Method ◽

Trust Region ◽

Affine Scaling ◽

Search Technique ◽

Region Method ◽

Bound Constrained Optimization ◽

Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

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A Derivative-Free Trust Region Algorithm with Nonmonotone Filter Technique for Bound Constrained Optimization

Mathematical Problems in Engineering ◽

10.1155/2018/5049027 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13

Author(s):

Jing Gao ◽

Jian Cao ◽

Yueting Yang

Keyword(s):

Constrained Optimization ◽

Optimization Problems ◽

Trust Region ◽

Computational Time ◽

Test Problems ◽

Trust Region Algorithm ◽

Filter Technique ◽

Derivative Free ◽

Bound Constrained Optimization ◽

Parameter Values

We propose a derivative-free trust region algorithm with a nonmonotone filter technique for bound constrained optimization. The derivative-free strategy is applied for special minimization functions in which derivatives are not all available. A nonmonotone filter technique ensures not only the trust region feature but also the global convergence under reasonable assumptions. Numerical experiments demonstrate that the new algorithm is effective for bound constrained optimization. Locally, optimal parameters with respect to overall computational time on a set of test problems are identified. The performance of the best choice of parameter values obtained by the algorithm we presented which differs from traditionally used values indicates that the algorithm proposed in this paper has a certain advantage for the nondifferentiable optimization problems.

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