On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

Deng, Xue; Sun, Wei

doi:10.1007/s11425-013-4677-y

Cited by 6 publications

(2 citation statements)

References 27 publications

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“…eir results extend the recent work of Conn et al [9] to fully linear models that have a nonlinear term. Xue and Sun [10] proposed a derivative-free trust region algorithm for constrained minimization problems with separable structure, where derivatives of the objective function are not available and cannot be directly approximated. ey constructed a quadratic interpolation model of the objective function around the current iterate and used the filter technique to ensure the feasibility and optimality of the iterative sequence.…”

Section: Problem Description Motivationmentioning

confidence: 99%

A Derivative-Free Affine Scaling LP Algorithm Based on Probabilistic Models for Linear Inequality Constrained Optimization

Zhao

Wang

Zhu

2022

Mathematical Problems in Engineering

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In this paper, a derivative-free affine scaling linear programming algorithm based on probabilistic models is considered for solving linear inequality constrainted optimization problems. The proposed algorithm is designed to build probabilistic linear polynomial interpolation models using only n + 1 interpolation points for the objective function and reduce the computation cost for building interpolation function. We build the affine scaling linear programming methods which use probabilistic or random models and affine matrix within a classical linear programming framework. The backtracking line search technique can guarantee monotone descent of the objective function, and by using this technique, the new iterative points are located within the feasible region. Under some reasonable conditions, the global and local fast convergence of the algorithm is shown, and the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

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Section: Problem Description Motivationmentioning

confidence: 99%

A Derivative-Free Affine Scaling LP Algorithm Based on Probabilistic Models for Linear Inequality Constrained Optimization

Zhao

Wang

Zhu

2022

Mathematical Problems in Engineering

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“…[3] published a derivative-free optimization method by using the Newton interpolation models. Xue and Sun [37] established the convergence analysis of derivative-free trust region algorithm for constrained optimization with separable structure. Zhang etc.…”

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confidence: 99%

A wedge trust region method with self-correcting geometry for derivative-free optimization

Zhang¹,

Sun²,

Sampaio³

et al. 2015

Numerical Algebra, Control &Amp; Optimization

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Recently, some methods for solving optimization problems without derivatives have been proposed. The main part of these methods is to form a suitable model function that can be minimized for obtaining a new iterative point. An important strategy is geometry-improving iteration for a good model, which needs a lot of calculations. Besides, Marazzi and Nocedal (2002) proposed a wedge trust region method for derivative free optimization. In this paper, we propose a new self-correcting geometry procedure with less computational efforts, and combine it with the wedge trust region method. The global convergence of new algorithm is established. The limited numerical experiments show that the new algorithm is efficient and competitive.2010 Mathematics Subject Classification. Primary: 65k05; Secondary: 90c30.

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A progressive barrier derivative-free trust-region algorithm for constrained optimization

et al. 2018

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On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

Cited by 6 publications

References 27 publications

A Derivative-Free Affine Scaling LP Algorithm Based on Probabilistic Models for Linear Inequality Constrained Optimization

A Derivative-Free Affine Scaling LP Algorithm Based on Probabilistic Models for Linear Inequality Constrained Optimization

A wedge trust region method with self-correcting geometry for derivative-free optimization

A progressive barrier derivative-free trust-region algorithm for constrained optimization

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