共查询到20条相似文献,搜索用时 31 毫秒
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Sándor Jenei 《Archive for Mathematical Logic》2003,42(5):489-514
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical
characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard
algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows
from their other axioms.
Received: 7 January 2002 / Revised version: 4 April 2002 /
Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics 相似文献
3.
Non-Interior continuation methods for solving semidefinite complementarity problems 总被引:13,自引:0,他引:13
There recently has been much interest in non-interior continuation/smoothing methods for solving linear/nonlinear complementarity
problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric
positive semidefinite real matrices. These extensions involve the Chen-Mangasarian class of smoothing functions and the smoothed
Fischer-Burmeister function. Issues such as existence of Newton directions, boundedness of iterates, global convergence, and
local superlinear convergence will be studied. Preliminary numerical experience on semidefinite linear programs is also reported.
Received: October 1999 / Accepted: April 2002 Published online: December 19, 2002
RID="⋆"
ID="⋆" This research is supported by National Science Foundation Grant CCR-9731273.
Key words. semidefinite complementarity problem – smoothing function – non-interior continuation – global convergence – local superlinear
convergence 相似文献
4.
In this paper we consider stochastic programming problems where the objective function is given as an expected value of a
convex piecewise linear random function. With an optimal solution of such a problem we associate a condition number which
characterizes well or ill conditioning of the problem. Using theory of Large Deviations we show that the sample size needed
to calculate the optimal solution of such problem with a given probability is approximately proportional to the condition
number.
Received: May 2000 / Accepted: May 2002-07-16 Published online: September 5, 2002
RID="★"
The research of this author was supported, in part, by grant DMS-0073770 from the National Science Foundation
Key Words. stochastic programming – Monte Carlo simulation – large deviations theory – ill-conditioned problems 相似文献
5.
Andrew J. Miller George L. Nemhauser Martin W.P. Savelsbergh 《Mathematical Programming》2003,94(2-3):375-405
We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This
model generalizes a number of structured MIP models previously studied, and it provides a relaxation of various capacitated
production planning problems and other fixed charge network flow problems. We analyze the polyhedral structure of the convex
hull of this model, as well as of a strengthened LP relaxation. Among other results, we present valid inequalities that induce
facets of the convex hull under certain conditions. We also discuss how to strengthen these inequalities by using known results
for lifting valid inequalities for 0–1 continuous knapsack problems.
Received: 30 October 2000 / Accepted: 25 March 2002 Published online: September 27, 2002
Key words. mixed integer programming – production planning – polyhedral combinatorics – capacitated lot–sizing – fixed charge network
flow
Some of the results of this paper have appeared in condensed form in ``Facets, algorithms, and polyhedral characterizations
of a multi-item production planning model with setup times', Proceedings of the Eighth Annual IPCO conference, pp. 318-332, by the same authors.
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian
State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors.
This research was also supported by NSF Grant No. DMI-9700285 and by Philips Electronics North America. 相似文献
6.
We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle that separates the
surface into two pieces. As a special case, every triangulation of the double torus in which every noncontractible cycle has
length at least 4 has a noncontractible cycle that separates the surface into two pieces.
Received: May 22, 2001 Final version received: August 22, 2002
RID="*"
ID="*" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070613
RID="†"
ID="†" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070430 相似文献
7.
In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs,
and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the
independent domination number can be computed in polynomial time within several classes of graphs, e.g., the class of locally
well-dominated graphs.
Received: September 13, 2001 Final version received: May 17, 2002
RID="*"
ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093)
RID="†"
ID="†" Supported by RUTCOR
RID="*"
ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093)
05C75, 05C69
Acknowledgments. The authors thank the referees for valuable suggestions. 相似文献
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We give a policy-improvement type algorithm to locate an optimal pure stationary strategy for discounted stochastic games
with perfect information. A graph theoretic motivation for our algorithm is presented as well.
Received: January 1998 / Accepted: May 2002 Published online: February 14, 2003
Key words. stochastic games – MDP – perfect information – policy iteration
Partially Funded by NSF Grant DMS 930-1052 and DMS 970-4951 相似文献
11.
We consider a quadratic cut method based on analytic centers for two cases of convex quadratic feasibility problems. In the
first case, the convex set is defined by a finite yet large number, N, of convex quadratic inequalities. We extend quadratic cut algorithm of Luo and Sun [3] for solving such problems by placing
or translating the quadratic cuts directly through the current approximate center. We show that, in terms of total number
of addition and translation of cuts, our algorithm has the same polynomial worst case complexity as theirs [3]. However, the
total number of steps, where steps consist of (damped) Newton steps, function evaluations and arithmetic operations, required
to update from one approximate center to another is , where ε is the radius of the largest ball contained in the feasible set. In the second case, the convex set is defined by
an infinite number of certain strongly convex quadratic inequalities. We adapt the same quadratic cut method for the first
case to the second one. We show that in this case the quadratic cut algorithm is a fully polynomial approximation scheme.
Furthermore, we show that, at each iteration, k, the total number steps (as described above) required to update from one approximate center to another is at most , with ε as defined above.
Received: April 2000 / Accepted: June 2002 Published online: September 5, 2002
Key words. convex quadratic feasibility problem – interior-point methods – analytic center – quadratic cuts – potential function 相似文献
12.
In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary
componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming
problems, as well as several models in Location and Regression Analysis are modeled within this framework.
In spite of its generality, this problem can be analyzed from a geometrical and a computational viewpoint, and a unified solution
methodology can be given. Indeed, a dual is derived, enabling us to describe the set of optimal solutions geometrically. Moreover,
Interior-Point methods are described which yield an $\varepsilon$-optimal solution in polynomial time.
Received: February 1999 / Accepted: March 2002 Published online: September 5, 2002
Key words. Goal programming – closest points – interior point methods – location – regression 相似文献
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It is proved that, for any ɛ>0 and n>n
0(ɛ), every set of n points in the plane has at most triples that induce isosceles triangles. (Here e denotes the base of the natural logarithm, so the exponent is roughly 2.136.) This easily implies the best currently known
lower bound, , for the smallest number of distinct distances determined by n points in the plane, due to Solymosi–Cs. Tóth and Tardos.
Received: February, 2002 Final version received: September 15, 2002
RID="*"
ID="*" Supported by NSF grant CCR-00-86013, PSC-CUNY Research Award 63382-00-32, and OTKA-T-032452
RID="†"
ID="†" Supported by OTKA-T-030059 and AKP 2000-78-21 相似文献
15.
A.S. Lewis 《Mathematical Programming》2003,97(1-2):155-176
Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical
challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich
blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of
some central mathematical ideas, outlined for the broad optimization community. I discuss the convex analysis of spectral
functions and invariant matrix norms, touching briefly on semidefinite representability, and then outlining two broader algebraic
viewpoints based on hyperbolic polynomials and Lie algebra. Analogous nonconvex notions lead into eigenvalue perturbation
theory. The last third of the article concerns stability, for polynomials, matrices, and associated dynamical systems, ending
with a section on robustness. The powerful and elegant language of nonsmooth analysis appears throughout, as a unifying narrative
thread.
Received: December 4, 2002 / Accepted: April 22, 2003
Published online: May 28, 2003
Key Words. eigenvalue optimization – convexity – nonsmooth analysis – duality – semidefinite program – subdifferential – Clarke regular
– chain rule – sensitivity – eigenvalue perturbation – partly smooth – spectral function – unitarily invariant norm – hyperbolic
polynomial – stability – robust control – pseudospectrum – H
∞
norm
Mathematics Subject Classification (2000): 90C30, 15A42, 65F15, 49K40 相似文献
16.
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined
in terms of games.
Received: 8 July 1999 Published online: 19 December 2002
RID="*"
ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him.
The authors thank the referee for helpful comments.
Mathematics Subject Classification (2000): 03E02, 05D10, 03E35
Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games 相似文献
17.
In this paper, we describe how to reformulate a problem that has second-order cone and/or semidefiniteness constraints in
order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth
and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided.
Received: March 10, 2001 / Accepted: January 18, 2002 Published online: September 27, 2002
Key Words. semidefinite programming – second-order cone programming – interior-point methods – nonlinear programming
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20 相似文献
18.
The relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem
is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known
results on the facial structure of the scheduling problem. Previous work on the facial structure has focused on describing
the convex hull of the set of feasible partial schedules, schedules in which not all jobs have to be started. The equivalence
between the characteristic vectors of this set and those of the set of feasible node packings in a graph whose structure is
determined by the parameters of the scheduling problem is established. The main contribution of this paper is to show that
the facet inducing inequalities for the convex hull of the set of feasible partial schedules that have integral coefficients
and right hand side 1 or 2 are the maximal clique inequalities and the maximally and sequentially lifted 5-hole inequalities
of the convex hull of the set of feasible node packings in this graph respectively.
Received: September 10, 2000 / Accepted: April 20, 2002 Published online: September 27, 2002
Key words. scheduling – node packing – polyhedral methods – facet defining graphs – lifted valid inequalities – facet inducing inequalities} 相似文献
19.
The authors of this paper recently introduced a transformation [4] that converts a class of semidefinite programs (SDPs)
into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application
of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods
to handle efficiently. Based on the transformation, we proposed a globally convergent, first-order (i.e., gradient-based)
log-barrier algorithm for solving a class of linear SDPs. In this paper, we discuss an efficient implementation of the proposed
algorithm and report computational results on semidefinite relaxations of three types of combinatorial optimization problems.
Our results demonstrate that the proposed algorithm is indeed capable of solving large-scale SDPs and is particularly effective
for problems with a large number of constraints.
Received: June 22, 2001 / Accepted: January 20, 2002 Published online: December 9, 2002
RID="†"
ID="†"Computational results reported in this paper were obtained on an SGI Origin2000 computer at Rice University acquired
in part with support from NSF Grant DMS-9872009.
RID="⋆"
ID="⋆"This author was supported in part by NSF Grants CCR-9902010, INT-9910084 and CCR-0203426
RID="⋆⋆"
ID="⋆⋆"This author was supported in part by NSF Grants CCR-9902010, INT-9910084 and CCR-0203113
RID="⋆⋆⋆"
ID="⋆⋆⋆"This author was supported in part by DOE Grant DE-FG03-97ER25331, DOE/LANL Contract 03891-99-23 and NSF Grant DMS-9973339.
Key Words. semidefinite program – semidefinite relaxation – nonlinear programming – interior-point methods – limited memory quasi-Newton
methods.
Mathematics Subject Classification (1991): 90C06, 90C27, 90C30. 相似文献
20.
Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints 总被引:2,自引:0,他引:2
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable
Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex
subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems
an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H?lder
one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the
global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional
variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.
Received: April 2002 / Accepted: December 2002
Published online: March 21, 2003
RID="⋆"
ID="⋆" This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, and RFBR 01–01–00587.
Key Words. global optimization – multiextremal constraints – local tuning – index approach 相似文献