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一类约束不可微优化问题的区间极大熵方法 总被引:23,自引:0,他引:23
本文研究求解不等式约束离散minimax问题的区间算法,其中目标函数和约束函数是 C~1类函数.利用罚函数法和极大熵函数思想将问题转化为无约束可微优化问题,讨论了极大熵函数的区间扩张,证明了收敛性等性质,提出了无解区域删除原则,建立了区间极大熵算法,并给出了数值算例.该算法是收敛、可靠和有效的. 相似文献
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§1 引言在非平衡态统计物理中,统计不可逆性与熵产生率是两个十分重要的概念.在[1]、[2]、[3]中,我们讨论了可以用马氏链描写的系统的可逆性与熵产生率,并证明一个平稳马氏链可逆的充分必要条件是熵产生率为零,进而又说明熵产生率是系统对时间的统计不可逆程度的一个刻划指标.但是,由于马氏链的状态空间的局限性,上述结果不能适应大量连续状态空间的物理问题研究的需要.为此,本文设法对一般的随机过程给出熵产生率的概率定义,并进而 相似文献
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噪声数据拟合与谱估计的极大互息原理 总被引:1,自引:0,他引:1
§1.引言由于极大熵方法的 AR 拟合和谱估计不考虑观测数据中噪声的影响,许多实际问题的谱分析和模型拟合效果不好.近年来[1]—[4],[12],[13]讨论了观测 相似文献
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Rembert Reemtsen 《Numerical Algorithms》1992,2(3):409-436
It is shown how the combined discretization and cutting plane method for general convex semi-infinite programming problems recently presented in [40] can be effectively implemented for the solution of minimax problems in the complex plane. In contrast to other approaches, the minimax problem does not have to be linearized. The performance of the algorithm is demonstrated by a number of highly accurate numerical examples. 相似文献
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T. Antczak 《Journal of Optimization Theory and Applications》2013,159(2):437-453
In the paper, we consider the exact minimax penalty function method used for solving a general nondifferentiable extremum problem with both inequality and equality constraints. We analyze the relationship between an optimal solution in the given constrained extremum problem and a minimizer in its associated penalized optimization problem with the exact minimax penalty function under the assumption of convexity of the functions constituting the considered optimization problem (with the exception of those equality constraint functions for which the associated Lagrange multipliers are negative—these functions should be assumed to be concave). The lower bound of the penalty parameter is given such that, for every value of the penalty parameter above the threshold, the equivalence holds between the set of optimal solutions in the given extremum problem and the set of minimizers in its associated penalized optimization problem with the exact minimax penalty function. 相似文献
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We consider minimax optimization problems where each term in the objective function is a continuous, strictly decreasing function of a single variable and the constraints are linear. We develop relaxation-based algorithms to solve such problems. At each iteration, a relaxed minimax problem is solved, providing either an optimal solution or a better lower bound. We develop a general methodology for such relaxation schemes for the minimax optimization problem. The feasibility tests and formulation of subsequent relaxed problems can be done by using Phase I of the Simplex method and the Farkas multipliers provided by the final Simplex tableau when the corresponding problem is infeasible. Such relaxation-based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure. We explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints; efficient algorithms exist to solve such problems. The relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources. There, instead of Phase I of the Simplex method, a max-flow algorithm is used to test feasibility and formulate new relaxed problems.Corresponding author.Work was partially done while visiting AT&T Bell Laboratories. 相似文献
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This paper describes and explores a maximum-entropy approach to continuous minimax problem, which is applicable in many fields, such as transportation planning and game theory. It illustrates that the maximum entropy approcach has easy framework and proves that every accumulation of {x_k} generated by maximum-entropy programming is -optimal solution of initial continuous minimax problem. The paper also explains BFGS or TR method for it. Two numerical exam.ples for continuous minimax problem are given 相似文献
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The minimax solution of a linear regulator problem is considered. A model representing a game situation in which the first player controls the dynamic system and selects a suitable, minimax control strategy, while the second player selects the aim of the game, is formulated. In general, the resulting differential game does not possess a saddle-point solution. Hence, the minimax solution for the player controlling the dynamic system is sought and obtained by modifying the performance criterion in such a way that (a) the minimax strategy remains unchanged and (b) the modified game possesses a saddle-point solution. The modification is achieved by introducing a regularization procedure which is a generalization of the method used in an earlier paper on the quadratic minimax problem. A numerical algorithm for determining the nonlinear minimax strategy in feedback form, in which Pagurek's result on open-loop and closed-loop sensitivity is used to nontrivially simplify the computational aspects of the problem, is presented and applied on a simple example. 相似文献
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《Operations Research Letters》1999,24(1-2):57-63
A polynomial time algorithm to obtain an exact solution for the equiweighted minimax location problem when the demand points are spread over a hemisphere is presented. It is shown that the solution of the minimax problem when the norm under consideration is geodesic is equivalent to solving a maximization problem using the Euclidean norm. 相似文献
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一类无约束离散Minimax问题的区间调节熵算法 总被引:3,自引:0,他引:3
LiSubei CaoDexin WangHaijun DengKazhong 《高校应用数学学报(英文版)》2004,19(1):37-43
In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C^1. The paper deals with this problem by means of taking the place of maximum-entropy function with adjustable entropy function. By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented. The relevant properties are proven, The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum-entropy algorithm. Both theoretical and numerical results show that the method is reliable and efficient. 相似文献
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带约束条件的离散Minimax问题的区间极大熵方法 总被引:4,自引:0,他引:4
给出了求解带约束条件Minimax问题的区间极大熵方法以及相关的算法,从数值例子来看,此算法是非常有效的。 相似文献