Fixed point quasiconvex subgradient method
Fixed point quasiconvex subgradient method
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DOI：
10.1016/j.ejor.2019.09.037
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
K. Hishinuma;H. Iiduka
中科院分区：
文献类型：
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作者：
K. Hishinuma;H. Iiduka
约束拟凸优化问题出现在许多领域，如经济学、工程学和管理学。其中，分式规划是一个重要的例子，它将利润/成本比等比率指标建模为分式目标函数。亚梯度方法及其变体是有效求解这些问题的有效方法。在这些应用中出现了许多复杂的约束集，在这些约束集上很难在实际时间内计算度量投影。这意味着现有的方法不能应用于复杂集合上的拟凸优化。同时，利用不动点理论，构造了一个不动点集与复杂约束集重合的可计算非膨胀映射。本文提出了一种利用可计算非扩展映射求解约束拟凸优化问题的算法。给出了常递减步长规则的收敛性分析。与现有算法的数值比较表明，即使现有算法的运行时间超过限制，本文算法也能稳定快速地运行。
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional objective functions, is an important instance. Subgradient methods and their variants are useful ways for solving these problems efficiently. Many complicated constraint sets onto which it is hard to compute the metric projections in a realistic amount of time appear in these applications. This implies that the existing methods cannot be applied to quasiconvex optimization over a complicated set. Meanwhile, thanks to fixed point theory, we can construct a computable nonexpansive mapping whose fixed point set coincides with a complicated constraint set. This paper proposes an algorithm that uses a computable nonexpansive mapping for solving a constrained quasiconvex optimization problem. We provide convergence analyses for constant diminishing step-size rules. Numerical comparisons between the proposed algorithm and an existing algorithm show that the proposed algorithm runs stably and quickly even when the running time of the existing algorithm exceeds the time limit.