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    王可心, 邵之江, LorenzTBiegler. 简约空间内点法的投影梯度可行性恢复[J]. 华东理工大学学报(自然科学版), 2014, (3): 332-337.
    引用本文: 王可心, 邵之江, LorenzTBiegler. 简约空间内点法的投影梯度可行性恢复[J]. 华东理工大学学报(自然科学版), 2014, (3): 332-337.
    WANG Ke-xin, SHAO Zhi-jiang, Lorenz T Biegler. Feasibility Restoration Based on Projected Gradient Methods for Reduced Space Barrier NLP Algorithm[J]. Journal of East China University of Science and Technology, 2014, (3): 332-337.
    Citation: WANG Ke-xin, SHAO Zhi-jiang, Lorenz T Biegler. Feasibility Restoration Based on Projected Gradient Methods for Reduced Space Barrier NLP Algorithm[J]. Journal of East China University of Science and Technology, 2014, (3): 332-337.

    简约空间内点法的投影梯度可行性恢复

    Feasibility Restoration Based on Projected Gradient Methods for Reduced Space Barrier NLP Algorithm

    • 摘要: 内点法作为一种高效的非线性规划算法,其简约空间算法实现尤其适于求解过程系统工程中的高维、低自由度优化问题,从而算法只需要在决策变量的低维空间寻求最优解,并且求解性能不依赖于模型的精确二阶导数信息,这对难以获得二阶导数或者二阶导数计算代价很大的复杂系统优化极为重要。为了保障简约空间内点法的全局收敛性,本文提出了与内点法共享空间分解结构的投影梯度可行性恢复算法。该算法结合了信赖域与线性搜索方法的优点,能够有效促进内点法的全局收敛。通过求解经典文献及CUTE/COPS算例库中的优化问题验证了本文提出算法的有效性。

       

      Abstract: Interior point methods are among the most efficient approach for nonlinear programming. Their implementation in reduced space framework is well suited for large problems with a few degrees of freedom, which often arise from chemical engineering applications where optimal solutions usually depend on a few decision variables. In addition, reduced space methods are attractive to optimization of process systems for which second order derivatives are not available or expensive to calculate. In order to guarantee global convergence of reduced space barrier methods, we propose a feasibility restoration algorithm based on projected gradient methods. This algorithm shares variable decompositions with barrier methods and combines the advantages of trust region and line search approaches. Numerical results of examples from literature and CUTE/COPS test sets demonstrate the performance of the proposed algorithm.

       

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