Steepest descent methods for multicriteria optimization
Steepest descent methods for multicriteria optimization
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DOI：
10.1007/s001860000043
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发表时间：
2000-08-01
影响因子：
1.2
通讯作者：
Svaiter, BF
中科院分区：
文献类型：
--
作者：
Fliege, J;Svaiter, BF
我们提出了无约束多目标优化的最速下降法和约束情况下的“可行下降方向”方法。在无约束的情况下，假设目标函数是连续可微的。在约束的情况下，目标和约束函数被假定为Lipshitz连续可微的，并假设一个约束资格。在这些条件下，它表明，这些方法收敛到一个点，满足一定的一阶必要条件的Pareto最优。这两种方法都不会对原始向量优化问题进行标量化。假设不同目标函数的排序信息和加权因子都是未知的。在单目标的情况下，我们检索的最速下降法和Zoutendijk的可行方向的方法，分别。
We propose a steepest descent method for unconstrained multicriteria optimization and a "feasible descent direction" method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuously differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuously differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto optimality. Both methods do not scalarize the original vector optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the Steepest descent method and Zoutendijk's method of feasible directions, respectively.