generalized convexity 中文意思是什麼
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In this thesis, the optimality sufficiency conditions and duality theory are discussed in multiobjective nonlinear programming involving ( f, a, p, d ) - convexity and generalized ( f, a, p, d ) - convexity. at that time, an algorithm is discussed for nonlinear multiobjective problem
本文主要討論了（ f ， ， ， d ） -凸及廣義（ f ， ， ， d ） -凸條件下非線性多目標規劃問題的最優性充分條件和對偶理論，同時，也探討了求解具有線性等式約束的非線性多目標規劃問題的一種新演算法。 -
Generalized increasing - decreasing functions and generalized convexity of the compound functions
遞減函數與復合函數的廣義凸性 -
Under the assuption of generalized subconvexlikeness, the optimality conditions of set - valued optimization problems in linear space are established by using obtained gordan - farkas type alternative theorem. under the assuption of near subconvexlikeness and - generalized convexity, the optimality conditions of set - valued optimization problems in linear topological space are established by using alternative theorem of near subconvexlikeness and obtained farkas - minkowski type alternative theorem. the concepts of super efficient solution and - super efficient solution are defined in normed space, and the optimality conditions of set - valued optimization problems are established under the assuption of semi - preinvexity
在廣義次似凸性假設下，利用已獲得的gordan - farkas型的擇一性定理，建立了線性空間中集值優化問題的最優性條件。在近次似凸和-廣義錐凸性假設下，利用近次似凸集值映射的擇一性定理和已獲得的farkas - minkowski型的擇一性定理，建立了線性拓撲空間中集值優化問題的最優性條件。 -
Under the different conditions of the constrained functions, dividing constrained sets properly, and under generalized ( f, ) convexity, the theorems of the weak duality, strong duality and strictly reverse duality are testified
依所給約束函數的不同條件來恰當劃分約束集，在廣義（ f ， ）凸性下，證明了弱對偶定理、強對偶定理以及嚴格逆對偶定理。 -
One is, based on answering the above open problem on a finite dimensional euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable - parameter three - step iterative algorithms for generalized set - valued variational inclusion problems by using - resolvent operator of set - valued mapping. two is to consider the convexity, closedness and boundedness of the solution set of general set - valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. three is to discuss directly the existence of solutions by using analytical methods for set - valued mixed quasi - variational - like inequalities and suggest a class of direct variable - parameter three - step iterative algorithms for solving generalized set - valued variational inclusions
研究分有三個方面：一是藉助于偏序理論在有限維歐氏空間中解決了上述公開問題，在此基礎上利用集值映射的-預解運算元，研究了廣義集值變分包含問題解的存在性、逼近解的全局誤差界、參數唯一解的靈敏性，並提出了一類變參數三步迭代演算法；二是藉助于圖收斂理論研究了一般集值變分包含問題解集的凸性、閉性和有界性以及參數解集的靈敏性；三是用分析的方法直接討論了集值混合擬類變分不等式問題解的存在性並提出了一類求解廣義集值變分包含問題的直接變參數三步迭代演算法。 -
Abstract : using the definitions of semi - locally star shaped set and generalized convexity for vector functions. we discuss the existence of efficient solutions for generalized multiobjective programming
文摘:本文利用1中的半局部星狀集和向量函數的廣義凸性，討論了一類廣義多目標規劃有效解的存在性。 -
Quasiconvex functions and various generalized convexity of functions play important roles in mathematical programming
擬凸函數及函數的各種廣義凸性，在數學規劃中起著重要作用。 -
Liu and wu ( ref. 26 ) presented sufficient conditions and proposed three dual models for the generalized fractional programming problem with - pseudoinvexity and - quasi - invexity in ref. 26. preda ( ref. 27 ) introduced generalized ( f, ) - convexity, an extension of f - convexity and generalized - convexiry ( ref. 28 - 29 ), relative results are also given for multiobjective programming problems
而preda在文獻[ 27 ]中，又引入了推廣的（ f ， ）一凸性，它是f ?凸性和推廣的?凸性（見文獻[ 28 - 29 ]的結合和延伸） ，同時給出了一些相關結果。 -
Measuring of market risks was generalized into beta coefficient, duration and convexity of bond risks, delta and var approach. methods of measuring credit risks were classified into classic models and modern credit measuring model. kmv model and creditmetrics model are the two most popular models in western countries
將市場風險的度量方法歸納為股票的風險度量beta系數，債券風險的度量持續期和凸性，金融衍生工具風險的度量delta等指標以及綜合度量市場風險的var方法；將信用風險的度量方法歸納為古典模型（專家制度和z計分模型）和現代信用風險度量模型（信用度量制模型等） 。 -
Abstract : in this paper, a kind of more generalized arcwise convex functions : p - arcwise convexity functions is defined. on the basis of definitions, sufficient conditions of multiobjective programming are proved
文摘:定義了一類更一般的弧式凸函數，並在此基礎上論證了其多目標規劃的充分性條件。 -
Furthermore, a mixed type dual for the primal problem is established and duality results are obtained. after that, the optimality sufficiency conditions and duality results for the nonlinear fractional programming problem are presented under generalized ( f, or, p, d ) - convexity assumptions
接著建立了含有等式約束和不等式約束的非線性多目標規劃問題的wolfe型對偶和mond - weir型對偶及原問題的混合類型對偶，並獲得了相應類型下的弱對偶定理和強對偶定理。 -
Under the assuption of - generalized convexity, relative interior is introduced, and a farkas - minkowski type alternative theorem is proved
在-廣義錐凸性假設下，引進相對內部，證明了farkas - minkowski型的擇一性定理。
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