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More Test Examples For Nonlinear Programming Codes

This paper proposes an affine scaling interior trust-region method in association with nonmonotone line search filter technique for solving nonlinear optimization problems subject to linear inequality constraints. Based on a Newton step which is derived from the complementarity conditions of linear inequality constrained optimization, a trust-region subproblem subject only to an ellipsoidal constraint is defined by minimizing a quadratic model with an appropriate quadratic function and scaling matrix. The nonmonotone schemes combining with trust-region strategy and line search filter technique can bring about speeding up the convergence progress in the case of high nonlinear. A new backtracking relevance condition is given which assures global convergence without using the switching condition used in the traditional line search filter technique. The fast local convergence rate of the proposed algorithm is achieved which is not depend on any external restoration procedure. The preliminary numerical experim...

An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization

A penalty method with trust-region mechanism for nonlinear bilevel optimization problem

In this work, we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed into two independent phases: a feasibility phase which reduces an infeasibility measure without evaluations of the objective function, and an optimality phase which reduces the objective function value. As the derivatives of the objective function are not available, the optimality step is computed by derivative-free trust-region internal iterations. Any technique to construct the trust-region models can be used since the gradient of the model is a reasonable approximation of the gradient of the objective function at the current point. Assuming this and classical assumptions, we prove that the full steps are efficient in the sense that near a feasible nonstationary ...

http://www.optimization-online.org/DB_FILE/2015/07/5024.pdf

Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

An active-set trust-region algorithm for solving warehouse location problem

In this paper, we propose a trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming. At current iteration, a trial step is formed as the sum of a normal step and a tangential step which is generated by trust-region subproblem and the step size is decided by interior backtracking line search together with filter methods. Then, the next iteration is determined. This is different from general trust-region methods in which the next iteration is determined by the ratio of the actual reduction to the predicted reduction. The global convergence analysis for this algorithm is presented under some reasonable assumptions and the preliminary numerical results are reported.

A trust-region algorithm combining line search filter technique for nonlinear constrained optimization

In this paper, a derivative-free trust region methods based on probabilistic models with new nonmonotone line search technique is considered for nonlinear programming with linear inequality constra

A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

In this paper, an affine-scaling derivative-free trust-region method with interior backtracking line search technique is considered for solving nonlinear systems subject to linear inequality constraints. The proposed algorithm is designed to take advantage of the problem structured by building polynomial interpolation models for each function in the nonlinear system function F. The proposed approach is developed by forming a quadratic model with an appropriate quadratic function and scaling matrix: there is no need to handle the constraints explicitly. By using both trust-region strategy and interior backing line search technique, each iteration switches to backtracking step generated by the trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. Under reasonable conditions, the global convergence and fast local convergence rate of the proposed algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.

An affine-scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints

In this paper, we propose a nonmonotone sequential quadratic programming-filter method for solving nonlinear equality constrained optimization. This new method has more flexibility for the acceptance of the trial step and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the global convergence properties. Further, the second-order correction step and nonmonotone reduction conditions are used to overcome Maratos effect so that quadratic local convergence is achieved. The numerical experiments are reported to show the effectiveness of the proposed algorithm.

Detong Zhu

Papers

An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization

A trust-region algorithm combining line search filter technique for nonlinear constrained optimization

A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

An affine-scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints

A nonmonotone SQP-filter method for equality constrained optimization