本文選題：極大極小系統(tǒng) + 全局最優(yōu)解��； 參考：《河北師范大學(xué)》2017年碩士論文

【摘要】：計(jì)算機(jī)科學(xué)、運(yùn)籌學(xué)和控制理論等方面的大量問(wèn)題都可以用極大極小系統(tǒng)來(lái)建立模型,例如數(shù)字電路、計(jì)算機(jī)網(wǎng)絡(luò)、自動(dòng)化制造廠等.對(duì)于帶有輸入結(jié)構(gòu)的生產(chǎn)系統(tǒng),經(jīng)�？紤]原料的輸入時(shí)間和機(jī)器的加工時(shí)間以及各機(jī)器工作的先后順序等.在滿足系統(tǒng)的限制條件的基礎(chǔ)上,希望對(duì)系統(tǒng)加以控制,使系統(tǒng)的工作達(dá)到最優(yōu)的狀態(tài).極大極小系統(tǒng),由非線性不可微分的極大極小函數(shù)來(lái)描述,極大極小函數(shù)包括取極大、取極小和加法三種運(yùn)算.極大極小系統(tǒng)是單極大系統(tǒng)的非線性拓展.相關(guān)文獻(xiàn)給出了極大極小函數(shù)在約束條件為1+2+···+9)=(7;4)≥0,4)=1,···,9);(7≥0的全局最優(yōu)解,得到的運(yùn)用控制向量的求解方法對(duì)解決極大極小函數(shù)的全局最優(yōu)解具有重要意義.本文利用極大極小函數(shù)的單極大投射和k控制向量進(jìn)一步研究了多個(gè)更加一般化的約束條件下極大極小函數(shù)全局最優(yōu)解的問(wèn)題.我們分別稱約束條件是2)(x)=(711+(722+···+(79)9)-(9≤0;5)≥0,5)=1,···,9);∨{2)(x)≤0}、2)4)(x)=(74)11+(74)22+···+(74)9)9)-Σ9)5)=1(75)≤0,4)=1,···,7);0≤5)≤1,5)=1,···,9);∨4)=1,···,7){2)4)(x)≤0}和2)4)(x)=(74)11+(74)22+···+(74)9)9)-(94)≤04)=1,···,7);5)≥0,5)=1,···,9);∨4)=1,···,7){2)4)(x)≤0}的三類極大極小函數(shù)的全局最優(yōu)解為第一類,第二類和第三類極大極小函數(shù)的全局最優(yōu)解.本文首先研究了在三類約束條件下的單極大系統(tǒng)的全局最優(yōu)解,得到了求解單極大系統(tǒng)的全局最優(yōu)解的充要條件.其次,在單極大系統(tǒng)的基礎(chǔ)上,通過(guò)極大投射將極大極小函數(shù)轉(zhuǎn)換為多個(gè)單極大函數(shù),又繼續(xù)研究了在三類特殊條件下極大極小函數(shù)的全局最優(yōu)解,得到了三類極大極小函數(shù)全局最優(yōu)解的充要條件,并給出了相關(guān)算法.
[Abstract]:A large number of problems in computer science, operational research and control theory can be modeled with minimax systems, such as digital circuits, computer networks, automated manufacturing plants, etc. For the production system with input structure, the input time of raw material, the processing time of machine and the sequence of work of each machine are often considered. On the basis of satisfying the limited conditions of the system, it is hoped that the system can be controlled to make the system work optimally. A minimax system is described by a nonlinear, non-differentiable minima function, which consists of three operations: maximum, minimax and addition. A minimax system is a nonlinear extension of a unipolar system. In the relevant literature, the global optimal solution of the minimax function with the constraint condition of 1 29) = (7 4) 鈮，

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