Mathematical programs with equilibrium constraints is a kind of specail opti - mzation problem , which besides equality constraints and inequality constraints it also contain complementarity constraints 帶有均衡約束的數(shù)學(xué)規(guī)劃問(wèn)題( mathematicalprogramswithequilibriumconstrains ,縮寫(xiě)為mpec )是一類(lèi)特殊的最優(yōu)化問(wèn)題,它的約束函數(shù)除了一般的等式和不等式約束之外,還包含有互補(bǔ)約束條件
Introduction of variational calculus and its application in the engineering optimal design , constrained / unconstrained optimal design problems , discrete optimal control and mathematical programming , practical examples of optimum design 先修課程:負(fù)責(zé)教授同意。變分微積分與最佳化之關(guān)系及其在工程最佳化上之應(yīng)用、端點(diǎn)條件、不連續(xù)最佳化程序、無(wú)限制及有限制條件最佳化問(wèn)題、直接法及實(shí)際最佳化設(shè)計(jì)應(yīng)用等。
Firstly , based on the classical theorem of limit analysis , the von mises yielding condition and finite element method technique , two common mathematical programs for the determination of the lower and upper bounds are built and solved by an iteration algorithm directly 首先,基于塑性極限載荷分析中的上下限定理和有限元離散技術(shù),推導(dǎo)和給出了一般結(jié)構(gòu)極限載荷上下限計(jì)算的數(shù)學(xué)規(guī)劃的普遍格式和相應(yīng)的積分?jǐn)?shù)值計(jì)算公式。
The status of the research for non - entirety analysis of arch dam and joint models commonly used were reviewed . the fem analysis for contact problem , i . e . , iterative method , contact constraints method and mathematical programming method , were summarized . 2 評(píng)述了拱壩結(jié)構(gòu)非整體性分析研究的現(xiàn)狀以及拱壩結(jié)構(gòu)分析中常用的接縫模型;進(jìn)一步從直接迭代法、接觸約束法和數(shù)學(xué)規(guī)劃法三個(gè)方面綜述了基于有限單元法的接觸問(wèn)題分析方法。
The travelling salesman problem ( tsp ) is always one of the most interesting topic in combinatorial majorizationo in the middle seventies , the appearance of the complexity theory of calculation and the development of mathematical programming have greatly improved the advancement of combinatorial majorization Tsp問(wèn)題一直是組合優(yōu)化中極富活力的研究課題之一。七十年代中期,計(jì)算復(fù)雜性理論的出現(xiàn)和數(shù)學(xué)規(guī)劃的發(fā)展大大推動(dòng)了組合優(yōu)化的前進(jìn)。
Process system optimization ( pso ) has become a major technology that helps companies in process industry to remain competitive . numerical derivatives play an important role in mathematical programming , which is the core area in pso 隨著計(jì)算機(jī)技術(shù)的飛速發(fā)展和企業(yè)自動(dòng)化程度的不斷提高,過(guò)程系統(tǒng)優(yōu)化已經(jīng)從純學(xué)術(shù)的理論發(fā)展成為能對(duì)工業(yè)起到巨大推動(dòng)作用的技術(shù)力量,成為過(guò)程工業(yè)企業(yè)保持競(jìng)爭(zhēng)力、在激烈的市場(chǎng)競(jìng)爭(zhēng)中立于不敗之地的主要技術(shù)手段。
In this thesis , we discuss mathematical programs with nonlinear complementarity constraints . because of the bad property of the equilibrium constraints , it is very difficult to study and solve it by the well - developed theory and methods for a standard smoothing nonlinear problems ( ssnp ) 本學(xué)位論文討論的是帶非線性互補(bǔ)約束規(guī)劃問(wèn)題,由于這類(lèi)問(wèn)題的約束條件的性質(zhì)很差,直接使用求解標(biāo)準(zhǔn)的光滑非線性約束優(yōu)化的方法和技術(shù)(如sqp )來(lái)求解,存在著一定的困難
In recent years , the theory and algorithm for semidefinite programming have developed greatly , and its most important applications are found in combinatorial optimization , system engineering and electrical engineering . semidefinite programming is a new and important research field in mathematical programming 近年來(lái)其理論和算法取得了很大的進(jìn)展,并且在組合優(yōu)化、系統(tǒng)工程和電子工程等領(lǐng)域得到廣泛的應(yīng)用,已經(jīng)成為數(shù)學(xué)規(guī)劃領(lǐng)域中一個(gè)新的活躍的研究方向
Furthermore , the comparison is made between eso and mathematical programming . in continuum structure optimization , eso is applied for topology optimization under the constraints of stress , displacement and frequency . in addition , eso is applied to the optimization for shells reinforced by ribs 在連續(xù)體結(jié)構(gòu)優(yōu)化方面,討論了幾類(lèi)約束下基于漸進(jìn)優(yōu)化方法的連續(xù)體拓?fù)鋬?yōu)化,這些約束分別是應(yīng)力約束,位移約束以及頻率約束;利用漸進(jìn)優(yōu)化方法,進(jìn)行了加筋板殼結(jié)構(gòu)的形狀優(yōu)化研究。
Having developed for half an century , the conventional optimization algorithms which are based on the operational research theory and some mathematical programming tools come into mature . such algorithms have been widely used in many fields due to their high efficiency and robustness . however , they usually require the optimized functions to be continuous even high order differentiable 這些在運(yùn)籌學(xué)( operationalresearch )和數(shù)學(xué)規(guī)劃工具( mathematicalprogramming )基礎(chǔ)上形成的最優(yōu)化算法,具有理論完備、算法效率高、穩(wěn)定性好等優(yōu)點(diǎn),因而在許多需要進(jìn)行優(yōu)化計(jì)算的場(chǎng)合被廣泛的使用。