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Some duality theorems in Nonsmooth Generalized Convex Programming

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Systems Science and Systems Engineering 1998年第3期8卷 64-72页

作者： ZENG Renying Department of Mathematics, Chongqing Teachers College,Chongqing 400047

In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x)  0 (i=1,…,m) g j(x)=0 (j=1,…, n), x ∈ Xand obtain various duality theorems. Where X is a Frechet space. f,g i(i=1,…, m) and h j(j=1, …, n) are functions from X to R 1.

关键词： frechet space (F ρ) invexity mathematical programming duality theorem

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

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Applied Mathematics(A Journal of Chinese Universities) 2008年第3期23卷 331-344页

作者： GAO Ying RONG Wei-dong School of Mathematical Sciences Inner Mongolia University Hohhot 010021 China

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.

关键词： operations research multiobjective generalized fractional programming optimality condition duality theorem generalized convexity

OPTIMIZATION AND duality OF ***

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Chinese Annals of Mathematics,Series B 1995年第4期16卷 499-508页

作者： YIN ZHIWEN LI YUANXI Department of Statistics and Operations Research Fudan UniversityShanghai 200433China.

This paper gives the definitions and some properties of E-directional derivate and ε-subgradientsof cone-convex function. mom them, the optimality conditions of local and global optimal point of unconstrained cone-d.... 详细信息

关键词： ε-directional derivate ε-subgradient Cone-d.c.function Optimality condition duality theorem

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

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Science China Mathematics 2008年第9期51卷 1561-1576页

作者： MA Xiang WANG Peng School of Mathematical Sciences Peking UniversityBeijing 100871China

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

关键词： spacelike Willmore surfaces polar surfaces adjoint transforms duality theorem Willmore 2-spheres Primary 53A30 Secondary 53B30