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71.
F. Thuijsman S. H. Tijs O. J. Vrieze 《Journal of Optimization Theory and Applications》1991,69(2):311-324
We examine stochastic games with finite state and action spaces. For the -discounted case, as well as for the irreducible limiting average case, we show the existence of trembling-hand perfect equilibria and give characterizations of those equilibria. In the final section, we give an example which illustrates that the existence of stationary limiting average equilibria in a nonirreducible stochastic game does not imply the existence of a perfect limiting average equilibrium.Support was provided by the Netherlands Organization for Scientific Research NWO via the Netherlands Foundation for Mathematics SMC, Project 10-64-10. 相似文献
72.
K. Marti 《Mathematical Methods of Operations Research》1992,36(3):259-294
In engineering and economics often a certain vectorx of inputs or decisions must be chosen, subject to some constraints, such that the expected costs (or loss) arising from the deviation between the outputA() x of a stochastic linear systemxA()x and a desired stochastic target vectorb() are minimal. Hence, one has the following stochastic linear optimization problem minimizeF(x)=Eu(A()x b()) s.t.xD, (1) whereu is a convex loss function on
m
, (A(), b()) is a random (m,n + 1)-matrix, E denotes the expectation operator andD is a convex subset of
n
. Concrete problems of this type are e.g. stochastic linear programs with recourse, error minimization and optimal design problems, acid rain abatement methods, problems in scenario analysis and non-least square regression analysis.Solving (1), the loss functionu should be exactly known. However, in practice mostly there is some uncertainty in assigning appropriate penalty costs to the deviation between the outputA ()x and the targetb(). For finding in this situation solutions hedging against uncertainty a set of so-called efficient points of (1) is defined and a numerical procedure for determining these compromise solutions is derived. Several applications are discussed. 相似文献
73.
G. Gopalakrishnan Nair 《Journal of Optimization Theory and Applications》1979,28(3):429-434
The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation
E
n
Euclideann-space
- f
Gradient off(x)
- 2
f
Hessian matrix
- (·)
T
Transpose of (·)
-
I
Index set {1, 2, ...,n}
- [x
i1
*(j)
]
Point around which search is made in the (j + 1)th iteration, i.e., [x
1l
*(j)
,x
2l
*(j)
,...,x
n1
*(j)
]
-
r
i
(i)
Range ofx
il
*(i)
in the (j + 1)th iteration
-
l
1
mini {r
i
(0)
}
-
l
2
mini {r
i
(0)
}
-
A
j
Region of search in thejth iteration, i.e., {x E
n:x
il
*(j-1)
–0.5r
i
(j-1)
x
ix
il
*(j-1)
+0.5r
i
(j-1)
,i I}
-
S
j
Closed sphere with center origin and radius
j
-
Reduction factor in each iteration
-
1–
- (·)
Gamma function
Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work. 相似文献
74.
Properties of the random search in global optimization 总被引:3,自引:0,他引:3
From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral
0
1
... 0/1 (x
1
2
+ ... +x
n
/2
)1/2
dx
1 ...dx
n. 相似文献
75.
Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle . 相似文献
76.
77.
This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation under certain boundary conditions on an angular domain The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company. 相似文献
78.
79.
80.
J. Mecke 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(1):45-53
The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length
distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case
is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated.
As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived.
Dedicated to the 80th birthday of Klaus Krickeberg 相似文献