At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文開始給出了凸函數(shù)的定義及等價定義，并證明了它們之間的等價關(guān)系免费看操网站；接著提出了凸函數(shù)的判定定理，對一個函數(shù)是否是凸函數(shù)提供判斷依據(jù)；然后對凸函數(shù)的運算性質(zhì)美女羞羞高潮视频免费首页、基本性質(zhì)、微分性質(zhì)一级黄啊啊啊啊网站、積分性質(zhì)四個方面的性質(zhì)進行了總結(jié)在线看日本，并給予了證明；最后證明了凸函數(shù)的幾個著名不等式詹森不等式一级性爱视频免费、赫爾德不等式人人操人人插人人搞、柯西不等式国产性爱一级视频，給出了這幾個不等式的一些應(yīng)用實例，并舉例說明凸函數(shù)的基本性質(zhì)和積分性質(zhì)在不等式證明過程中的重要作用欧美A片在线中文字幕。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文開始給出了凸函數(shù)的定義及等價定義美女被cao出水免费观看网站，并證明了它們之間的等價關(guān)系；接著提出了凸函數(shù)的判定定理欧美一级高清片，對一個函數(shù)是否是凸函數(shù)提供判斷依據(jù)激情小说图片自拍；然后對凸函數(shù)的運算性質(zhì)、基本性質(zhì)欧洲性生活无码在线、微分性質(zhì)干8网址、積分性質(zhì)四個方面的性質(zhì)進行了總結(jié)，并給予了證明亚洲国产福利精品；最后證明了凸函數(shù)的幾個著名不等式詹森不等式91三级毛片在线观看不卡无风险、赫爾德不等式、柯西不等式和閔可夫斯基不等式以及這幾個不等式的應(yīng)用又黄又大又粗的视频，并舉例說明凸函數(shù)的基本性質(zhì)和積分性質(zhì)在不等式證明過程中的重要作用无码粉嫩小泬无套在线观看免费。

Two new rules represented in equality for Demyanov difference: the Demyanov difference of summations of two pairs of convex compact complementary sets;the Demyanov difference of a set, which is the convex hull of finite number of convex compact sets, and a convex compact set complementary to these sets,are given.

為此給出了兩個關(guān)于Demyanov差的新的用等式表述的運算法則：兩個彼此互補的凸緊集對的和的Demyanov差，有限個凸緊集的凸包和與這些凸緊集正交互補的凸緊集的Demyanov差隐私偷拍偷窥AV合集。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

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Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有關(guān)凸模糊映射的理論：建立了關(guān)于凸模糊映射的Jensen不等式www.免费视频在线观看、模糊正齊次映射亚洲中文字幕一区二区三区营、凸模糊映射的下卷積、右數(shù)乘和凸包等概念国产Av人人澡夜夜澡人人爽，利用模糊數(shù)的參數(shù)化表示av优选精品久久国产，給出了相應(yīng)的定理；在反模糊數(shù)空間性生活视频一级片，對凸模糊映射的共軛也作了探討久久性激情，證明了凸模糊映射的共軛集合和共軛映射都是凸的；最后對凸模糊映射的次梯度国产免费A片在线网址、次微分和微分等概念進行了研究自拍少妇亚洲，為模糊極值理論打下了基礎(chǔ)。

Based on the previous work of other researchers, we presented the definition of global convex: a surface is globally convex if it happens to be the surface of a convex body or part of the surface of a convex body.

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As pointed out by Deville et al., a class of connected row-convex constraints is shown to be tractable.

相接行凸(connected row-convex爽爽的电影AV片，簡稱CRC)約束網(wǎng)絡(luò)是Deville等人提出的一類易處理問題91人妻PORNY九色最新社区。

To solve the optimization problems, apply the DCA （difference of convex functions algori-thms） which is a general framework for nonconvex continuous optimization. This leads to a successive linear programming algorithm with finite convergence.

為解決優(yōu)化問題，應(yīng)用了突函數(shù)差異算法（difference of convex functions algorithms水蜜桃在线无码视频免费，DCA）這一進行非突連續(xù)優(yōu)化的通用框架丝袜剧情国产AV办公室，致使連續(xù)線性規(guī)劃算法有限收斂。

In this paper, a varieties of concepts of compactness of sets and sunsets are introduced in a complex locally convex space, which are respectively the generalizations of the known sunsets and convex sets. By establishing the relationship between restricted p-centers of a set in a complex locally convex space and restricted Chebyshev centers of the corresponding set in the quotient space with respect to ker, characterizations and uniqueness of restricted p-centers of sets in a complex locally convex space are obtained. These results are better than any other known ones when we restrict them in real normed linear spaces and real locally convex space.

本文首先在復(fù)局部凸空間中引入了幾種緊性及幾種太陽集的概念WWW尤物在线，它們分別是已有緊性和凸集概念的推廣91插插插插；然后通過建立局部凸空間中集的限制p-中心和關(guān)于ker的商空間中對應(yīng)集的限制Chebyshev中心的關(guān)系，來研究局部凸空間中集的限制p-中心問題国产精品永久久，本文即使是在實賦范空間和在實局部凸空間中所得的結(jié)果都分別是有關(guān)已知結(jié)果的深化和推廣一级迷奸影院。

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