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非光滑B-预不变凸优化问题的解集刻画
  • ISSN号：1672-6693
  • 期刊名称：《重庆师范大学学报：自然科学版》
  • 时间：0
  • 分类：O221.2[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]重庆师范大学数学学院,重庆400047
  • 相关基金：The National Science Foundation of China(No.11171363);the Special Fund of Chongqing Key Laboratory(No.CSTC2011KLORSE02);the Education Committee Research Foundation of Chongqing(No.KJ110625)
作者： 万轩[1], 赵克全[1]
关键词： 非光滑B-预不变凸优化, Clarke次微分, 解集, nonsmooth B-preinvex optimization Clarke s subdifferential solution sets
中文摘要：

给出了具有不等式约束的非光滑B一预不变凸优化问题的最优解集的各种刻画。首先，利用Clarke次微分建立了该优化问题最优解的充分必要条件；再讨论了该优化问题在其解集S上的一个性质：最后建立了该优化问题解集的5种等价形式，即S={x∈M｜∈（，q（z，z）〉=0，j{∈伊，（z）=（zEMI〈}，q（z，z）〉≥0，｜{EOCf（x）}={z∈M｜（{，71（x，z））=〈}，q（z，z）〉，j{Ec（z），}Eaf（x））={x∈Ml（{，71（x，z））≥（}，叩（z，z）〉，j{Ec（z），E扩，（z）}={z∈M｜（，7（z，z））=〈，q（z，z）〉=0，j{Ec（z），}EoCf（x）}，并举例验证这5个集合都相等，为s={o}。

英文摘要：

In this paper, various characterizations lems with inequality constrains are given. Firstly condition for this kind of optimization problem; strained B-preinvex optimization proble; finally, is, i.e. S = {0} . of optimal solution sets of nonsmooth B-preinvex optimization prob- , making use of Clarke＇s subdifferential, we establish the optimality secondly, we presented a property about the solution set S of con five equivalent characterizations of the solution set are obtained, that = （x An example is given E MI to illustrate that five solution sets are

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期刊信息
  • 《重庆师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:重庆市教育委员会
  • 主办单位:重庆师范大学
  • 主编：杨新民
  • 地址：重庆市沙坪坝区
  • 邮编：400047
  • 邮箱：cqnuj@cqnu.edu.cn
  • 电话：023-65362431
  • 国际标准刊号：ISSN：1672-6693
  • 国内统一刊号：ISSN：50-1165/N
  • 邮发代号:78-34
  • 获奖情况:
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  • 被引量:4584