共查询到18条相似文献,搜索用时 375 毫秒
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本文研究了一类多目标控制问题的混合对偶性.利用函数的广义V-不变凸性条件,得出了关于有效解的弱对偶定理、强对偶定理和严格逆对偶定理,推广了多目标控制问题的对偶性结论. 相似文献
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焦合华 《数学的实践与认识》2010,40(16)
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n和b的B-(p,γ)-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. 相似文献
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在一类锥约束单目标优化问题的一阶对偶模型基础之上,建立了锥约束多目标优化问题的二阶和高阶对偶模型.在广义凸性假设下,给出了弱对偶定理,在Kuhn-Tucker约束品性下,得到了强对偶定理.最后,在弱对偶定理的基础上,利用Fritz-John型必要条件建立了逆对偶定理. 相似文献
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《数学的实践与认识》2010,(16)
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. 相似文献
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本文研究了一类含有锥约束多目标变分问题的广义对称对偶性.利用函数的(F,ρ)-不变凸性的条件,得出了多目标变分问题关于有效解的弱对偶定理、强对偶定理和逆对偶定理,将多目标变分问题的对称对偶性理论推广到含有锥约束的广义对称对偶性上来. 相似文献
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考虑一类多目标控制优化问题,这里允许端点在某些曲面上任意地变化.利用控制问题的广义Hamilton函数解的必要条件,构作两种形式的对偶问题模型;在ρ-不变凸假设之下证明了弱对偶定理、强对偶定理和逆对偶定理. 相似文献
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本文主要研究E-凸函数的若干性质,引入E-凸多目标规划的定义,建立E-凸多目标规划的Mond-Weir型对偶问题,并在E.凸条件假设下,证明E-凸多目标规划的弱对偶性、直接对偶性及逆对偶性. 相似文献
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In this paper we first establish a Lagrange multiplier condition characterizing a regularized Lagrangian duality for quadratic
minimization problems with finitely many linear equality and quadratic inequality constraints, where the linear constraints
are not relaxed in the regularized Lagrangian dual. In particular, in the case of a quadratic optimization problem with a
single quadratic inequality constraint such as the linearly constrained trust-region problems, we show that the Slater constraint
qualification (SCQ) is necessary and sufficient for the regularized Lagrangian duality in the sense that the regularized duality
holds for each quadratic objective function over the constraints if and only if (SCQ) holds. A new theorem of the alternative
for systems involving both equality constraints and two quadratic inequality constraints plays a key role. We also provide
classes of quadratic programs, including a class of CDT-subproblems with linear equality constraints, where (SCQ) ensures
regularized Lagrangian duality. 相似文献
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关于E-凸函数和E-凸规划的错误结论 总被引:6,自引:0,他引:6
最近Youness在文[1]建立了一类E-凸函数和一类E-凸规划,并分析和给出了他们的主要性质。本文通过6个反例说明文[1]关于E-凸函数和E-凸规划的大部分结论是错误的。 相似文献
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给出一对锥约束多目标非线性规划的二阶对称对偶问题,以及二阶F凸函数类的概念.在二阶F凸假设下证明了真有效解的对偶性质———弱对偶性、强对偶性及逆对偶性. 相似文献
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We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal (2010) are discussed. 相似文献
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In this paper are defined new first- and second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds between the primal and dual problems. We introduce a notion of a second-order WD-invex problem with inequality constraints. The class of WD-invex problems is strictly included in the class of second-order ones. We derive that the first-order duality results are satisfied in the second-order case. 相似文献