共查询到20条相似文献,搜索用时 2 毫秒
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Dominika Bogusz 《Journal of Optimization Theory and Applications》2013,156(3):650-682
We consider an infinite-horizon optimal control problem with the cost functional described either by an integral over an unbounded interval (a Lebesgue integral) or by a limit of integrals (an improper Lebesgue integral). We prove some theorems on the existence of solutions to such problems. The proofs are based on appropriate lower closure theorems and some extensions of Olech’s theorem on the lower semicontinuity of an integral functional; these extensions cover the cases of functionals described by an integral over an unbounded interval and by a limit of integrals. 相似文献
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高峰 《应用数学与计算数学学报》1997,11(2):89-96
本文研究了单约束条件的非凸极小问题的对偶形式,我们的结论是通过变换,可以化成无缝对偶情形,同时我们研究了多约束条件的同类问题的处理方法。 相似文献
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A question of flow around an obstacle leads to an optimal control problem. If an optimum path exists, then it is calculable from the Pontryagin principle. The optimum is verified to be reached, using a discretization of the problem. 相似文献
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Hongwei Lou 《Applied Mathematics and Optimization》2009,59(1):75-97
Relaxed controls are widely used to analyze the existence of optimal controls in the literature. Though there are many optimal
control problems admitting no optimal control, rare examples were shown. This paper will solve a particular optimal control
problem by analyzing the optimal relaxed controls, showing the ideas we used to study such kind of problems.
This work was supported by NSFC (No. 10671040), FANEDD (No. 200522) and NCET (No. 06-0359). 相似文献
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Journal of Applied and Industrial Mathematics - We consider an optimal control problem for some mathematical problem of a chemical reactor. We prove the existence of a solution to the system in... 相似文献
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Srinivas Sridharan William M. McEneaney Mile Gu Matthew R. James 《Applied Mathematics and Optimization》2014,70(3):469-510
The process of obtaining solutions to optimal control problems via mesh based techniques suffers from the well known curse of dimensionality. This issue is especially severe in quantum systems whose dimensions grow exponentially with the number of interacting elements (qubits) that they contain. In this article we develop a min-plus curse-of-dimensionality-free framework suitable to a new class of problems that arise in the control of certain quantum systems. This method yields a much more manageable complexity growth that is related to the cardinality of the control set. The growth is attenuated through \(\max \) -plus projection at each propagation step. The method’s efficacy is demonstrated by obtaining an approximate solution to a previously intractable problem on a two qubit system. 相似文献
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M. S. Nikol'skii 《Differential Equations》2005,41(11):1602-1608
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M. Majewski 《Journal of Optimization Theory and Applications》2006,128(3):635-651
In this paper, some results concerning the existence of optimal solutions to an optimal control problem are derived. The problem involves a quasilinear hyperbolic differential equation with boundary condition and a nonlinear integral functional of action. The assumption of convexity, under which the main theorem is proved, is not connected directly with the convexity of the functional of action. In the proof, the implicit function theorem for multimappings is used.Communicated by L. D. Berkovitz 相似文献
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讨论了一类可允许控制策略满足单调非降条件的随机最优控制问题,给出了值函数v(t,x,y,)满足一类受梯度限制的Hamilton-Jacobi-Bellman(HJB)方程:max{Lv(t,x,y), v(t,x,y)/ y}=0,其中Lv(t,x,y)= v/ t b(t,x,y,) v/ x 1/2σ2(t,x,y) 2v/ x2 f(t,x,y).借助粘性解的思想,定义了该类HJB方程的粘性解并在此意义下证明了v(t,x,y)是唯一粘性解,这类方程在随机控制,金融数学等领域内有重要应用. 相似文献
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We consider the ordinary differential equation $$x^2 u''=axu'+bu-c \bigl(u'-1\bigr)^2, \quad x\in(0,x_0), $$ with $a\in\mathbb{R}, b\in\mathbb{R}$ , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave. 相似文献
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Tolulope Latunde Joseph Oluwaseun Richar Opeyemi Odunayo Esan Damilola Deborah Dare 《Journal of Nonlinear Modeling and Analysis》2021,3(3):335-348
In this work, we analyse the transportation problem of a real-life situation by obtaining the optimal feasible solutions, thus carrying out the sensitivity analysis of the problem. The work utilises the data obtained from the Asejire and Ikeja plants of Coca-Cola company, aiming to aid decision-making regarding the best possible options to satisfy customers at the barest minimum cost of transportation. Rerunning the optimization of a problem is an expensive scheme for gathering and obtaining enough data required for a problem. Thus, to minimize the transportation cost, the sensitivity analysis of parameters is a good tool to determine the behaviour of some input parameters where the values of these parameters are varied arbitrarily such that optimal results are verified. Maple 18 Software is used to solve the problem and the result obtained is compared with the values evaluated from northwest corner method, least cost method and Vogel''s approximation method. The study critically shows how a little change in a unit or more of any model parameter affects the expected results. 相似文献
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On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics 总被引:2,自引:0,他引:2
Dalibor Lukáš 《Applications of Mathematics》2004,49(5):441-464
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards. 相似文献