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1.
Portfolio managers in the international fixed income markets must address jointly the interest rate risk in each market and
the exchange rate volatility across markets. This paper develops integrated simulation and optimization models that address
these issues in a common framework. Monte Carlo simulation procedures generate jointly scenarios of interest and exchange
rates and, thereby, scenarios of holding period returns of the available securities. The portfolio manager’s risk tolerance is incorporated either through a utility function or
a (modified) mean absolute deviation function. The optimization models prescribe asset allocation weights among the different
markets and also resolve bond-picking decisions. Therefore several interrelated decisions are cast in a common framework.
Two models – an expected utility maximization and a mean absolute deviation minimization – are implemented and tested empirically
in tracking a composite index of the international bond markets. Backtesting over the period January 1997 to July 1998 illustrate
the efficacy of the optimization models in dealing with uncertainty and tracking effectively the volatile index. Of particular
interest is the empirical demostration that the integrative models generate portfolios that dominate the portfolios obtained
using classical disintegrated approaches.
Received: November 24, 1998 / Accepted: October 1, 2000?Published online December 15, 2000 相似文献
2.
In this paper, we focus on the restoration of images that have incomplete data in either the image domain or the transformed
domain or in both. The transform used can be any orthonormal or tight frame transforms such as orthonormal wavelets, tight
framelets, the discrete Fourier transform, the Gabor transform, the discrete cosine transform, and the discrete local cosine
transform. We propose an iterative algorithm that can restore the incomplete data in both domains simultaneously. We prove
the convergence of the algorithm and derive the optimal properties of its limit. The algorithm generalizes, unifies, and simplifies
the inpainting algorithm in image domains given in Cai et al. (Appl Comput Harmon Anal 24:131–149, 2008) and the inpainting
algorithms in the transformed domains given in Cai et al. (SIAM J Sci Comput 30(3):1205–1227, 2008), Chan et al. (SIAM J Sci
Comput 24:1408–1432, 2003; Appl Comput Harmon Anal 17:91–115, 2004). Finally, applications of the new algorithm to super-resolution
image reconstruction with different zooms are presented.
R. H. Chan’s research was supported in part by HKRGC Grant 400505 and CUHK DAG 2060257.
L. Shen’s research was supported by the US National Science Foundation under grant DMS-0712827.
Z. Shen’s research was supported in part by Grant R-146-000-060-112 at the National University of Singapore. 相似文献
3.
In the radio channel assignment problems considered here, we must assign a ‘channel’ from the set 1,2,... of positive integers
to each of n transmitters, and we wish to minimise the span of channels used, subject to the assignment leading to an acceptable level
of interference. A standard form of this problem is the ‘constraint matrix’ model. The simplest case of this model (the 0,
1 case) is essentially graph colouring. We consider here a random model for the next simplest case (with lengths 0, 1 or 2),
and determine the asymptotic behaviour of the span of channels needed as n→∞. We find that there is a ‘phase change’ in this behaviour, depending on the probabilities for the different lengths. 相似文献
4.
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
5.
We consider the problem of preemptively scheduling a set of n jobs on m (identical, uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby
incur job-dependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize
the preemptive makespan on the m machines plus the sum of the penalties of the jobs rejected.
We provide a complete classification of these scheduling problems with respect to complexity and approximability. Our main
results are on the variant with an arbitrary number of unrelated machines. This variant is APX-hard, and we design a 1.58-approximation
algorithm for it. All other considered variants are weakly -hard, and we provide fully polynomial time approximation schemes
for them. Finally, we argue that our results for unrelated machines can be carried over to the corresponding preemptive open
shop scheduling problem with rejection.
Received: October 30, 2000 / Accepted: September 26, 2001 Published online: September 5, 2002
Key words. scheduling – preemption – approximation algorithm – worst case ratio – computational complexity – in-approximability
Supported in part by the EU Thematic Network APPOL, Approximation and Online Algorithms, IST-1999-14084
Supported by the START program Y43-MAT of the Austrian Ministry of Science. 相似文献
6.
For a conic linear system of the form Ax ∈ K, K a convex cone, several condition measures have been extensively studied in the last dozen years. Among these, Renegar’s condition
number is arguably the most prominent for its relation to data perturbation, error bounds, problem geometry, and computational complexity
of algorithms. Nonetheless, is a representation-dependent measure which is usually difficult to interpret and may lead to overly conservative bounds
of computational complexity and/or geometric quantities associated with the set of feasible solutions. Herein we show that
Renegar’s condition number is bounded from above and below by certain purely geometric quantities associated with A and K; furthermore our bounds highlight the role of the singular values of A and their relationship with the condition number. Moreover, by using the notion of conic curvature, we show how Renegar’s
condition number can be used to provide both lower and upper bounds on the width of the set of feasible solutions. This complements
the literature where only lower bounds have heretofore been developed. 相似文献
7.
The computational complexity of the following type of problem is studied. Given a geometric graph G=( P, S) where P is a set of points in the Euclidean plane and S a set of straight (closed) line segments between pairs of points in P, we want to know whether G possesses a crossingfree subgraph of a special type. We analyze the problem of detecting crossingfree spanning trees, one factors and two factors in the plane. We also consider special restrictions on the slopes and on the lengths of the edges in the subgraphs.Klaus Jansen acknowledges support by the Deutsche Forschungsgemeinschaft. Gerhard J. Woeginger acknowledges support by the Christian Doppler Laboratorium für Diskrete Optimierung. 相似文献
8.
We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that
the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together
with the so-called cut inequalities yield an integer programming formulation of the problem in the space of the natural design
variables. We then study the polytope associated with that problem and describe further classes of valid inequalities. We
give necessary and sufficient conditions for these inequalities to be facet defining. We study the separation problem associated
with these inequalities. In particular, we show that the cycle inequalities can be separated in polynomial time when K≤4. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results. 相似文献
9.
An algorithm is developed for minimizing nonsmooth convex functions. This algorithm extends Elzinga–Moore cutting plane algorithm
by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our
method is to Elzinga–Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. Instead of lower approximations
used in proximal bundle methods, the present approach is based on some objects regularizing translated functions of the objective
function. We propose some variants and using some academic test problems, we conduct a numerical comparative study with Elzinga–Moore
algorithm and two other well-known nonsmooth methods.
相似文献
10.
We consider a special class of two-stage stochastic integer programming problems with binary variables appearing in both stages. The class of problems we consider constrains the second-stage variables to belong to the intersection of sets corresponding to first-stage binary variables that equal one. Our approach seeks to uncover strong dual formulations to the second-stage problems by transforming them into dynamic programming (DP) problems parameterized by first-stage variables. We demonstrate how these DPs can be formed by use of binary decision diagrams, which then yield traditional Benders inequalities that can be strengthened based on observations regarding the structure of the underlying DPs. We demonstrate the efficacy of our approach on a set of stochastic traveling salesman problems. 相似文献
11.
We present a predictor–corrector non–interior path following algorithm for the monotone linear complementarity problem based
on Chen–Harker–Kanzow–Smale smoothing techniques. Although the method is modeled on the interior point predictor–corrector
strategies, it is the first instance of a non–interior point predictor–corrector algorithm. The algorithm is shown to be both
globally linearly convergent and locally quadratically convergent under standard hypotheses. The approach to global linear
convergence follows the authors’ previous work on this problem for the case of ( P
0+ R
0) LCPs. However, in this paper we use monotonicity to refine our notion of neighborhood of the central path. The refined neighborhood
allows us to establish the uniform boundedness of certain slices of the neighborhood of the central path under the standard
hypothesis that a strictly positive feasible point exists.
Received September 1997 / Revised version received May 1999?Published online December 15, 1999 相似文献
12.
In this paper, we construct a q-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where q ranges over the set of integers. When q = 1, it coincides with the Witt-Burnside ring introduced by Dress and Siebeneicher (Adv. Math. 70, 87–132 (1988)). To achieve
our goal we first show that there exists a q-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the case q = 1, q-deformed Witt-Burnside rings and necklace rings always come equipped with inductions and restrictions. We also study their
properties. As a byproduct, we prove a conjecture due to Lenart (J. Algebra. 199, 703-732 (1998)). Finally, we classify up to strict natural isomorphism in case where G is an abelian profinite group.
The author gratefully acknowledges support from the following grants: KOSEF Grant # R01-2003-000-10012-0; KRF Grant # 2006-331-C00011. 相似文献
13.
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly
finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary
abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated
categories; we apply Gentle–Todorov’s theorem to obtain short proofs of a classical result by Ringel and a recent result by
Krause and Solberg.
This project is partially supported by China Postdoctoral Science Foundation (No.s 20070420125 and 200801230). The author
also gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong. 相似文献
14.
We use recent advances in circle-packing theory to develop a constructive method for the approximation of an analytic function F: Ω → C by circle packing maps providing we have only been given Ω F’ dΩ, and the set of critical points of F. This extends the earlier results of Carter and Rodin and of Colin de Verdière and Mathéus, for functions F with no critical points.
The author gratefully acknowledges support of the Tennessee Science Alliance and the National Science Foundation. Research
at MSRI is supported in part by Grant No. DMS-9022140. 相似文献
15.
We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s
method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us
to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining
convergence rate results.
The research of O.P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grant 475647/2006-8, CNPq Grant 302618/2005-8, PRONEX–Optimization(FAPERJ/CNPq)
and IMPA.
The research of B.F. Svaiter was supported in part by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization(FAPERJ/CNPq). 相似文献
16.
As discovered recently, Li and Wang’s 1997 treatment of semicontinuity for frames does not faithfully reflect the classical
concept. In this paper we continue our study of semicontinuity in the pointfree setting. We define the pointfree concepts
of lower and upper regularizations of frame semicontinuous real functions. We present characterizations of extremally disconnected
frames in terms of these regularizations that allow us to reprove, in particular, the insertion and extension type characterizations
of extremally disconnected frames due to Y.-M. Li and Z.-H. Li [ Algebra Universalis 44 (2000), 271–281] in the right semicontinuity context. It turns out that the proof of the insertion theorem becomes very easy
after having established a number of basic results regarding the regularizations. Notably, our extension theorem is a much
strengthened version of Li and Li's result and it is proved without making use of the insertion theorem.
The first and second named authors acknowledge financial support from the Ministry of Education and Science of Spain and FEDER
under grant MTM2006-14925-C02-02. The first named
author also acknowledges financial support from the University of the Basque Country under
grant UPV05/101. The third named author acknowledges financial support from the Centre of
Mathematics of the University of Coimbra/FCT. 相似文献
17.
In this paper, we introduce the exact order of Hoffman’s error bounds for approximate solutions of elliptic quadratic inequalities.
Elliptic quadratic inequalities are closely related to Chebyshev approximation of vector-valued functions (including complex-valued
functions). The set of Chebyshev approximations of a vector-valued function defined on a finite set is shown to be Hausdorff
strongly unique of order exactly 2
s
for some nonnegative integer s. As a consequence, the exact order of Hoffman’s error bounds for approximate solutions of elliptic quadratic inequalities
is exactly 2
-s
for some nonnegative integer s. The integer s, called the order of deficiency (which is computable), quantifies how much the Abadie constraint qualification is violated
by the elliptic quadratic inequalities.
Received: April 15, 1999 / Accepted: February 21, 2000?Published online July 20, 2000 相似文献
18.
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features multivariate stochastic benchmarking constraints based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the decision-based random outcome vector of interest is preferable to a specified benchmark with respect to the multivariate polyhedral conditional value-at-risk or a multivariate stochastic order relation. In this case, the classical decomposition methods cannot be used directly due to the complicating multivariate stochastic benchmarking constraints. We propose an exact unified decomposition framework for solving these two classes of optimization problems and show its finite convergence. We apply the proposed approach to a stochastic network design problem in the context of pre-disaster humanitarian logistics and conduct a computational study concerning the threat of hurricanes in the Southeastern part of the United States. The numerical results provide practical insights about our modeling approach and show that the proposed algorithm is computationally scalable. 相似文献
19.
In this paper, we use integer programming (IP) to compute minimal forecast horizons for the classical dynamic lot-sizing problem (DLS). As a solution approach for computing forecast horizons, integer programming has been largely ignored by the research community. It is our belief that the modelling and structural advantages of the IP approach coupled with the recent significant developments in computational integer programming make for a strong case for its use in practice. We formulate some well-known sufficient conditions, and necessary and sufficient conditions (characterizations) for forecast horizons as feasibility/optimality questions in 0–1 mixed integer programs. An extensive computational study establishes the effectiveness of the proposed approach. 相似文献
20.
We consider a problem of decision under uncertainty with outcomes distributed over time. We propose a rough set model based
on a combination of time dominance and stochastic dominance. For the sake of simplicity we consider the case of traditional
additive probability distribution over the set of states of the world, however, we show that the model is rich enough to handle
non-additive probability distributions, and even qualitative ordinal distributions. The rough set approach gives a representation
of decision maker’s time-dependent preferences under uncertainty in terms of “ if…, then…” decision rules induced from rough approximations of sets of exemplary decisions. 相似文献
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