亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Duality of Semi-infinite Programming via Augmented Lagrangian

        2021-10-20 03:26:18SUKe蘇珂WANGChen王晨LINYumeng林雨萌
        應(yīng)用數(shù)學(xué) 2021年4期
        關(guān)鍵詞:王晨

        SU Ke(蘇珂),WANG Chen(王晨),LIN Yumeng(林雨萌)

        (1.College of Mathematics and Information Science,Hebei University,Baoding 071002,China;2.Hebei Province Key Laboratory of Machine Learning and Computational Intelligence,Baoding 071002,China)

        Abstract:In this paper,we mainly study the dual problem of the nonconvex semi-infinite programming problem with inequality constraints.It is well known that there is usually a duality gap in constructing duality problem using the ordinary Lagrangian function.To eliminate the duality gap,we construct an augmented Lagrangian function,then discuss its duality.Under reasonable assumptions,the strong duality theorem between the primal problem and the augmented Lagrangian dual problem holds.Finally,an example is given to verify the presented results.

        Key words:Semi-infinite programming;Nonconvex;Duality;Augmented Lagrangian function

        1.Introduction

        Semi-infinite programming,which contains a finite number of variablesx=(x1,··· ,xn)∈Rnon a feasible set and an infinite number of constraints,is a common optimization problem.Semi-infinite programming can be used in Chebyshev approximation[1],optimal control and transportation problem[2].It also can be found in molecular biotechnology,such as finding optimized complex control strategy in some special control system[3].

        In the article,we consider the augmented Lagrangian dual problem of nonconvex semiinfinite programming with inequality constraints.For convex semi-infinite programming,there are many literatures[4?6]have discussed it’s duality theory and optimal solution properties.A primal-dual augmented Lagrangian method for solving an equality constrained minimization problem was considered by Armand[7].For convex programming with finite number of constraints,theoretical properties of the augmented Lagrangian duality were systematically analysed by using the conjugate duality theory in[8].In general form,the idea of constructing augmented Lagrangian functions was presented by Rockafellar and Wets[9].Similarly,in an infinite dimensional setting,Azimov[10]constructed a sharp augmented Lagrangian function to obtain some strong duality results.For solving constrained nonconvex optimization problem,a new sharp augmented Lagrangian-based global optimization method[11]was presented.

        Most of the existing literatures are based on Lagrangian function to obtain the dual problem of constrained programming,while the augmented Lagrangian function is less used to study the dual problem.Motivated and inspired by the research of semi-infinite programming duality theory,in this paper,we construct an augmented Lagrangian function,then we give sufficient conditions for the strong duality of nonconvex semi-infinite programming.

        The structure of this paper is as follows.In Section 2,we introduce some basic knowledge and constructed augmented lagrangian function.In Section 3,we discuss the duality between the primal problem and the dual problem and give an example.We give a conclusion in Section 4.

        2.Preliminaries

        3.Duality

        4.Conclusion

        Duality theory has the most profound influence on semi-infinite programming.However,there is usually a duality gap between primal problem and its dual problem by the standard Lagrangian function.Therefore,in this paper,the augmented Lagrangian function is constructed for nonconvex semi-infinite programming and its dual problem is systematically discussed.Under the suitable conditions,the strong duality holds,that is,there is no duality gap.This method is a generalization of the existing method.

        猜你喜歡
        王晨
        區(qū)塊鏈技術(shù)嵌入下數(shù)字政府成本會(huì)計(jì)系統(tǒng)構(gòu)建
        MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS*
        Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit-phonon hybrid system?
        X線與CT在下肢骨關(guān)節(jié)骨折中的診斷價(jià)值分析
        穿梭武漢疫情“火線”
        民生周刊(2020年8期)2020-04-20 11:18:24
        Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system:A polaron-transformed Redf ield approach*
        王晨
        寶藏(2018年1期)2018-04-18 07:39:20
        大學(xué)有機(jī)化學(xué)教學(xué)中學(xué)案的作用探討
        火車上蹭坐
        蹭座
        蜜桃tv在线免费观看| 国产三级黄色在线观看| 亚洲日本视频一区二区三区| 人妖国产视频一区二区| 欧美成人看片一区二区三区尤物| 亚洲av伊人久久综合密臀性色| 日韩在线视精品在亚洲| 国产精品黄色在线观看| 80s国产成年女人毛片| 伊人狠狠色丁香婷婷综合| 欧美伊人亚洲伊人色综| 羞涩色进入亚洲一区二区av| 亚洲av天堂在线视频| 日韩av精品国产av精品| 在线观看国产一区亚洲bd| 亚洲av中文字字幕乱码软件 | 成品人视频ww入口| 亚洲av无码乱观看明星换脸va| 久久99久久99精品免观看女同 | 久久精品国产69国产精品亚洲| 亚洲中文字幕无码天然素人在线 | 一本大道久久东京热无码av| 久久久噜噜噜噜久久熟女m| 人妻激情偷乱视频一区二区三区 | 国产粉嫩美女一区二区三| 在线观看国产视频你懂得| 亚洲av福利无码无一区二区| 亚洲av美女在线播放啊| 人妻丰满熟妇一二三区| 亚洲熟妇色自偷自拍另类| 免费人成再在线观看网站| 狠狠亚洲超碰狼人久久老人| 精品三级国产一区二区三| 国产xxxxx在线观看| 亚洲V在线激情| 国产视频一区2区三区| 亚洲av无码片vr一区二区三区| 色吧综合网| 久久网站在线免费观看| 亚洲熟女精品中文字幕| 国产免费又色又爽又黄软件|