准凸最小化的子梯度投影法

IF 0.8 3区数学 Q2 MATHEMATICS Positivity Pub Date : 2024-09-05 DOI:10.1007/s11117-024-01082-z

Juan Choque, Felipe Lara, Raúl T. Marcavillaca

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引用次数: 0

摘要

本文提供了一种用于准凸最小化问题的子梯度投影方法。通过使用强次微分，证明了所提算法生成的序列，在与凸函数与凸次微分所需的假设相同的情况下，收敛于适当的、下半连续的、强准凸函数（Polyak 在 Soviet Math 7:72-75, 1966 中的意义）的最小化问题的解。此外，还提供了迭代的准线性收敛率，扩展了一般准凸情况下的类似结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A subgradient projection method for quasiconvex minimization

In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By employing strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous, and strongly quasiconvex function (in the sense of Polyak in Soviet Math 7:72–75, 1966), under the same assumptions as those required for convex functions with the convex subdifferentials. Furthermore, a quasi-linear convergence rate of the iterates, extending similar results for the general quasiconvex case, is also provided.

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.