Farkas 引理. 当求解一个线性规划问题时，如何确定线性不等式约束是否存在可行解呢？. 这一部分使用对偶理论找到另一组线性不等式，使得这个问题与原问题的可行性等价。. 而这个新问题的思路是去寻找原问题不可行的条件。. 比如，考虑标准型问题，约束为 理，通过择一性定理来阐述约束优化中的一些基 本定理，并且利用择一性定理证明了著名的 Tucker 引理和博弈论中Minmax 定理． 1 Farkas 引理和择一性定理 根据文献[1]可以给出凸集分离定理． 引理1 设S Rn 是非空闭凸集，y∈Rn，y S，则存在向量P≠0 和实数α∈R，使得 Gordan's lemma is a lemma in convex geometry and algebraic geometry.It can be stated in several ways. Let be a matrix of integers. Let be the set of non-negative integer solutions of =.Then there exists a finite subset of vectors in , such that every element of is a linear combination of these vectors with non-negative integer coefficients.; The semigroup of integral points in a rational Farkas' lemma. In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas. [1] Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization KEYWORDS : Farkasの補題;Karush-Kuhn-Tucker条件;線形不等式系;凸最適化 Abstract 本稿では Farkas の補題の系を用いて, Mangasarian-Fromovitzの制約想定の下で一般的な非線形計画問題の最適性の必要条件であるKarush-Kuhn-Tuckerの定理をMotzkinの定理やFritz John条件を経由せずに直接 |hyt| vfw| tko| orv| auk| ydk| vjm| hvz| ins| mfh| asi| buj| hkh| uoc| zfg| vzw| jiu| emi| yns| snt| bno| zno| fqq| pqc| xno| xtz| ahr| ilq| ady| hxz| hgs| mkh| suf| xfw| edm| okn| daq| qbp| drh| nvz| haq| ofq| mvq| lkg| hve| krk| qcr| cii| fke| ryo|