B-(p,r)-不变凸规划的最优性条件及混合型对偶  

Optimality Conditions and Mixed-type Duality for Programming with B-(p,r)-Invexity

作　　者：焦合华[1] 

机构地区：[1]长江师范学院数学与计算机学院,重庆408003

出　　处：《数学的实践与认识》2010年第16期138-143,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10171118);重庆市教委科学技术研究基金(KJ051307)

摘　　要：函数的广义凸性在数学规划及数学规划的对偶理论中起着非常重要的作用.在一种函数的广义凸性—关于η和b的B-(p,r)-不变凸性的假设下,讨论了一类含有无穷多分式函数的约束广义分式规划及其对偶的某些问题:首先,给出并证明了这类约束广义分式规划的一个最优性充分条件,接着,针对这一类广义分式规划,提出了它的一个混合型对偶,然后又在适当的条件下,进一步给出并证明了相应的弱对偶定理,强对偶定理以及严格逆对偶定理.Generalized convexity of functions play an important role in mathematical programming and its dual theory. In this paper, under a generalized convexity -B- （p, r）-invexity with respect to η and b assumptions, the dual and some questions of a class of constrained generalized fractional programming containing infinite fractional functions are discussed. First, a sufficient condition is presented and proved for this constrained generalized fractional programming. Second, a dual for this class constrained generalized fractional programming is put forward, and then, the results about weak duality, strong duality and strictly reverse duality are further given and proved under suitable conditions.

关 键 词：广义分式规划 混合型对偶 B-(p  r)-不变凸性 最优性条件 

分 类 号：O221.2[理学—运筹学与控制论]