共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper is an attempt to provide a connection between qualitative matrix theory and linear programming. A linear program
is said to be sign-solvable if the set of sign patterns of the optimal solutions is uniquely determined by the sign patterns of A, b, and c. It turns out to be NP-hard to decide whether a given linear program is sign-solvable or not. We then introduce a class of
sign-solvable linear programs in terms of totally sign-nonsingular matrices, which can be recognized in polynomial time. For
a linear program in this class, we devise an efficient combinatorial algorithm to obtain the sign pattern of an optimal solution
from the sign patterns of A, b, and c. The algorithm runs in O(mγ) time, where m is the number of rows of A and γ is the number of all nonzero entries in A, b, and c. 相似文献
2.
Yinyu Ye 《Mathematical Programming》2006,106(2):339-363
We present complexity results on solving real-number standard linear programs LP(A,b,c), where the constraint matrix
the right-hand-side vector
and the objective coefficient vector
are real. In particular, we present a two-layered interior-point method and show that LP(A,b,0), i.e., the linear feasibility problem A
x = b and x ≥ 0, can be solved in in O(n
2.5
c(A)) interior-point method iterations. Here 0 is the vector of all zeros and c(A) is the condition measure of matrix A defined in [25]. This complexity iteration bound is reduced by a factor n from that for general LP(A, b, c) in [25]. We also prove that the iteration bound will be further reduced to O(n
1.5
c(A)) for LP(A, 0, 0), i.e., for the homogeneous linear feasibility problem. These results are surprising since the classical view has been that
linear feasibility would be as hard as linear programming.
This author was supported in part by NSF Grants DMS-9703490 and DMS-0306611 相似文献
3.
Tianze Wang 《数学学报(英文版)》1995,11(2):156-167
Denote byE(X) the number of integersn X which are not a sum of a prime and a square. Set = 1 – 0.994428b, whereb min(0.9365/c
3, 0.02578/c
4),c
3,c
4 being given in Lemma 8. The resultE(x) x
is proved in this paper.Project Supported by the National Natural Science Foundation of China. 相似文献
4.
C. E. Carroll 《Aequationes Mathematicae》1982,24(1):97-109
Leta
1,b
1,c
1,A
1 anda
2,b
2,c
2,A
2 be the sides and areas of two triangles. Ifa=(a
1
p
+a
2
p
)1/p
,b=(b
1
p
+b
2
p
)1/p
,c=(c
1
p
+c
2
p
)1/p
, and 1p4, thena, b, c are the sides of a triangle and its area satisfiesA
p/2A
1
p/2
+A
2
p/2
. If obtuse triangles are excluded,p>4 is allowed. For convex cyclic quadrilaterals, a similar inequality holds. Also, leta, b, c, A be the sides and area of an acute or right triangle. Iff(x) satisfies certain conditions,f(a),f(b),f(c) are the sides of a triangle having areaA
f, which satisfies (4A
f/3)1/2f((4A/3)1/2). 相似文献
5.
We consider the general optimization problem (P) of selecting a continuous function x over a -compact Hausdorff space T to a metric space A, from a feasible region X of such functions, so as to minimize a functional c on X. We require that X consist of a closed equicontinuous family of functions lying in the product (over T) of compact subsets Y
t
of A. (An important special case is the optimal control problem of finding a continuous time control function x that minimizes its associated discounted cost c(x) over the infinite horizon.) Relative to the uniform-on-compacta topology on the function space C(T,A) of continuous functions from T to A, the feasible region X is compact. Thus optimal solutions x
* to (P) exist under the assumption that c is continuous. We wish to approximate such an x
* by optimal solutions to a net {P
i
}, iI, of approximating problems of the form minxX
i
c
i(x) for each iI, where (1) the net of sets {X
i
}
I
converges to X in the sense of Kuratowski and (2) the net {c
i
}
I
of functions converges to c uniformly on X. We show that for large i, any optimal solution x
*
i
to the approximating problem (P
i
) arbitrarily well approximates some optimal solution x
* to (P). It follows that if (P) is well-posed, i.e., limsupX
i
* is a singleton {x
*}, then any net {x
i
*}
I
of (P
i
)-optimal solutions converges in C(T,A) to x
*. For this case, we construct a finite algorithm with the following property: given any prespecified error and any compact subset Q of T, our algorithm computes an i in I and an associated x
i
* in X
i
* which is within of x
* on Q. We illustrate the theory and algorithm with a problem in continuous time production control over an infinite horizon. 相似文献
6.
7.
Carlo Sbordone 《Milan Journal of Mathematics》1989,59(1):173-184
We prove a regularity theorem for quasiminima of a degenerate functional of the type
, whereA (t) has non polynomial growth andb(x) is a weight belonging to theA, class of Muckenhoupt.
Si dimostra un teorema di regolarità per i quasiminimi di un funzionale degenere del tipo
, conA(t) ad andamento non polinomiale eb(x) peos della classeA, di Muckenhoupt.
(Conferenza tenuta il 13 novembre 1989) 相似文献
(Conferenza tenuta il 13 novembre 1989) 相似文献
8.
We give the exact closed form solution of the following ordinary differential equation:
which is a modified logistic one, wherein x(t) is the population of a homogeneous species x at time t. Other than integrating the above nonlinear differential equation by means of Mathieu functions of the first kind, we also
provide a condition of a couple of inequalities involving a, b, c, h and x
0 whose fulfillment is sufficient to ensure that a bounded solution for x(t) there exists.
相似文献
9.
For a given objective functionw(x, a) onX × A, a maximizinga=(x) has to be determined for eachx in the totally ordered setX. We give conditions onw such that there is a monotone which can be computed recursively ifA is finite. 相似文献
10.
G. Kuba 《Acta Mathematica Hungarica》2000,87(1-2):173-178
For fixed c > 1 and for arbitrary and independent a,b ≧ 1 let Z
2|b( cosh(x/a)−c) ≦ y < 0}. We investigate the asymptotic behaviour of R(a,b) for a,b → ∞. In the special case b = o(a
5/6) the lattice rest has true order of magnitude
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
We study the Cauchy problem for second order hyperbolic operators in the Gevrey classes where H(t,x) is given by the limit of a finite sum of functions such as a(t)b(x) with a(t) ≥ 0, b(x) ≥ 0. As a result, for any given positive integer N, we give an example H(t,x) which depends not only on t but also on x such that the Cauchy problem for P is well posed in the Gevrey class of order N. 相似文献
12.
Grgoire Nadin 《Journal de Mathématiques Pures et Appliquées》2009,92(3):232-262
This paper is concerned with the existence of pulsating traveling fronts for the equation:(1)
∂tu−(A(t,x)u)+q(t,x)u=f(t,x,u),