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A SQP Method for Inequality Constrained Optimization

Acta Mathematicae Applicatae Sinica 2002年第1期18卷 77-84页

作者： Ju-liang ZHANG, Xiang-sun ZHANGInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

In this paper, a new SQP method for inequality constrained optimization is proposed and the global convergence is obtained under very mild conditions.

关键词： SQP method global convergence inequality constrained optimization nondifferentiable exact penalty function

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AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2003年第4期16卷 494-505页

作者： ZHANGJuliang ZHANGXiangstm ZHUOXinjian DepartmentofManagementScienceandEngineering SchoolofEconomicsandManagementTsinghuaUniversityBeijin9100084China InstituteofAppliedMathematics AcademyofMathematicsandSystemsSciencesChineseAcademyofSciencesBeijing100080China SchoolofInformationEngineering BeijingUniversityofPostsandTelecommunicationsBeijing100876China

In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced ***, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent.

关键词： equality constrained optimization global convergence trust region method superlinear convergence nondifferentiable exact penalty function maratos effect

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