共查询到10条相似文献,搜索用时 93 毫秒
1.
Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in
which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO
as applied to uncertain linear, conic quadratic and semidefinite programming. For these cases, computationally tractable robust
counterparts of uncertain problems are explicitly obtained, or good approximations of these counterparts are proposed, making
RO a useful tool for real-world applications. We discuss some of these applications, specifically: antenna design, truss topology
design and stability analysis/synthesis in uncertain dynamic systems. We also describe a case study of 90 LPs from the NETLIB
collection. The study reveals that the feasibility properties of the usual solutions of real world LPs can be severely affected
by small perturbations of the data and that the RO methodology can be successfully used to overcome this phenomenon.
Received: May 24, 2000 / Accepted: September 12, 2001?Published online February 14, 2002 相似文献
2.
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on
a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples
of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Received: 6 July 1999 / Revised version: 19 April 2000 /?Published online: 14 June 2001 相似文献
3.
A. V. Domrin 《Theoretical and Mathematical Physics》2000,124(1):872-886
We consider a static one-dimensional Ginzburg-Landau equation (on a line segment or a circle) involving a large parameter
λ. We show that as λ→∞, there exist solutions whose asymptotic behavior resembles the behavior of the two-dimensional vortex
solutions.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 18–35, July, 2000. 相似文献
4.
R. Pytlak 《Numerische Mathematik》2002,91(2):319-321
Summary. We show that the example given in [Dai, Y., Yuan, Y. (1999): Global convergence of the method of shortest residuals, Numerische
Mathematik 83, 581–598] does not contradict the results of [Pytlak, R. (1994): On the convergence of conjugate gradient algorithms,
IMA J. Numerical Analysis 14, 443–460].
Received September 9, 2000 / Revised version received November 28, 2000 / Published online July 25, 2001 相似文献
5.
Based on the authors’ previous work which established theoretical foundations of two, conceptual, successive convex relaxation
methods, i.e., the SSDP (Successive Semidefinite Programming) Relaxation Method and the SSILP (Successive Semi-Infinite Linear Programming)
Relaxation Method, this paper proposes their implementable variants for general quadratic optimization problems. These problems
have a linear objective function c
T
x to be maximized over a nonconvex compact feasible region F described by a finite number of quadratic inequalities. We introduce two new techniques, “discretization” and “localization,”
into the SSDP and SSILP Relaxation Methods. The discretization technique makes it possible to approximate an infinite number
of semi-infinite SDPs (or semi-infinite LPs) which appeared at each iteration of the original methods by a finite number of
standard SDPs (or standard LPs) with a finite number of linear inequality constraints. We establish:?•Given any open convex set U containing F, there is an implementable discretization of the SSDP (or SSILP) Relaxation Method
which generates a compact convex set C such that F⊆C⊆U in a finite number of iterations.?The localization technique is for the cases where we are only interested in upper bounds on the optimal objective value (for
a fixed objective function vector c) but not in a global approximation of the convex hull of F. This technique allows us to generate a convex relaxation of F that is accurate only in certain directions in a neighborhood of the objective direction c. This cuts off redundant work to make the convex relaxation accurate in unnecessary directions. We establish:?•Given any positive number ε, there is an implementable localization-discretization of the SSDP (or SSILP) Relaxation Method
which generates an upper bound of the objective value within ε of its maximum in a finite number of iterations.
Received: June 30, 1998 / Accepted: May 18, 2000?Published online September 20, 2000 相似文献
6.
A. J. Zaslavski 《Applied Mathematics and Optimization》2000,42(3):291-313
In this work we analyze the structure of optimal solutions for a class of infinite-dimensional control systems. We are concerned
with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends
the result of Carlson, Haurie, and Jabrane to a situation where the trajectories are not necessarily bounded. Also, we show
that an optimal trajectory defined on an interval [0,τ] is contained in a small neighborhood of the optimal steady-state in the weak topology for all t ∈ [0,τ] \backslash E , where E \subset [0,τ] is a measurable set such that the Lebesgue measure of E does not exceed a constant which depends only on the neighborhood of the optimal steady-state and does not depend on τ .
Accepted 26 July 2000. Online publication 13 November 2000. 相似文献
7.
How fast are the particles of super-Brownian motion? 总被引:5,自引:1,他引:4
Peter Mörters 《Probability Theory and Related Fields》2001,121(2):171-197
In this paper we investigate fast particles in the range and support ofsuper-Brownian motion in the historical setting. In
this setting eachparticle of super-Brownian motion alive at time t is represented by apath w:[0,t]→ℝ
d
and the state of historical super-Brownian motionis a measure on the set of paths. Typical particles have Brownian paths,however
in the uncountable collection of particles in the range of asuper-Brownian motion there are some which at exceptional times
movefaster than Brownian motion. We determine the maximal speed of allparticles during a given time period E, which turns out to be afunction of the packing dimension of E. A path w in the support ofhistorical super-Brownian motion at time t is called a-fast if . Wecalculate the Hausdorff dimension of the set of a-fast paths in thesupport and the range of historical super-Brownian motion. A valuabletool in the proofs is a uniform dimension
formula for the Browniansnake, which reduces dimension problems in the space of stopped paths to dimension problems on the
line.
Received: 27 January 2000 / Revised version: 28 August 2000 / Published online: 24 July 2001 相似文献
8.
9.
In this paper we try to generalize the notion of a minimal polynomial of an algebraic number to a class of transcendental
elements from where is the completion of the algebraic closure of ℚ in ℂ, relative to the spectral norm on : ([PPP], [PPZ1], [PPZ2], [PPZ3]).
Received: 2 July 2002 / Revised version: 13 January 2003 Published online: 20 March 2003
Mathematics Subject Classification (2000): 11R99 相似文献
10.
Thorsten Koch 《Operations Research Letters》2004,32(2):138-142
With standard linear programming solvers there is always some uncertainty about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the exact optimal objective values for all NETLIB problems. 相似文献