共查询到20条相似文献,搜索用时 875 毫秒
1.
On the core of ordered submodular cost games 总被引:5,自引:0,他引:5
A general ordertheoretic linear programming model for the study of matroid-type greedy algorithms is introduced. The primal
restrictions are given by so-called weakly increasing submodular functions on antichains. The LP-dual is solved by a Monge-type
greedy algorithm. The model offers a direct combinatorial explanation for many integrality results in discrete optimization.
In particular, the submodular intersection theorem of Edmonds and Giles is seen to extend to the case with a rooted forest
as underlying structure. The core of associated polyhedra is introduced and applications to the existence of the core in cooperative
game theory are discussed.
Received: November 2, 1995 / Accepted: September 15, 1999?Published online February 23, 2000 相似文献
2.
Benchmarking optimization software with performance profiles 总被引:9,自引:6,他引:3
We propose performance profiles — distribution functions for a performance metric — as a tool for benchmarking and comparing
optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.
Received: February 2001 / Accepted: May 2001?Published online October 2, 2001 相似文献
3.
This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality
constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods
for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the
iterates is progressively enforced thanks to shift variables and an exact penalty approach. Global and q-superlinear convergence is obtained for a fixed penalty parameter; global convergence to the analytic center of the optimal
set is ensured when the barrier parameter tends to zero, provided strict complementarity holds.
Received: December 21, 2000 / Accepted: July 13, 2001?Published online February 14, 2002 相似文献
4.
Consider the problem of routing the electrical connections among two large terminal sets in circuit layout. A realistic model
for this problem is given by the vertex-disjoint packing of two Steiner trees (2VPST), which is known to be NP-complete. This
work presents an investigation on the 2VPST polyhedra. The main idea is to start from facet-defining inequalities for a vertex-weighted
Steiner tree polyhedra. Some of these inequalities are proven to also define facets for the packing polyhedra, while others
are lifted to derive new important families of inequalities, including proven facets. Separation algorithms are provided.
Branch-and-cut implementation issues are also discussed, including some new practical techniques to improve the performance
of the algorithm. The resulting code is capable of solving problems on grid graphs with up to 10000 vertices and 5000 terminals
in a few minutes.
Received: August 1999 / Accepted: January 2001?Published online April 12, 2001 相似文献
5.
This paper deals with exponential neighborhoods for combinatorial optimization problems. Exponential neighborhoods are large sets of feasible solutions whose size grows
exponentially with the input length. We are especially interested in exponential neighborhoods over which the TSP (respectively,
the QAP) can be solved in polynomial time, and we investigate combinatorial and algorithmical questions related to such neighborhoods.?First,
we perform a careful study of exponential neighborhoods for the TSP. We investigate neighborhoods that can be defined in a
simple way via assignments, matchings in bipartite graphs, partial orders, trees and other combinatorial structures. We identify
several properties of these combinatorial structures that lead to polynomial time optimization algorithms, and we also provide
variants that slightly violate these properties and lead to NP-complete optimization problems. Whereas it is relatively easy
to find exponential neighborhoods over which the TSP can be solved in polynomial time, the corresponding situation for the
QAP looks pretty hopeless: Every exponential neighborhood that is considered in this paper provably leads to an NP-complete optimization problem for the QAP.
Received: September 5, 1997 / Accepted: November 15, 1999?Published online February 23, 2000 相似文献
6.
Christian Prins 《Mathematical Methods of Operations Research》2000,52(3):389-411
For more than two machines, and when preemption is forbidden, the computation of minimum makespan schedules for the open-shop
problem is NP-hard. Compared to the flow-shop and the job-shop, the open-shop has free job routes which lead to a much larger
solution space, to smaller gaps between the optimal makespan and the lower bounds, and to disappointing results for the algorithms
based on the disjunctive graph model. For instance, the best existing branch and bound method cannot solve some 7 ×7 hard
instances to optimality, and all published metaheuristics (working by reversing some disjunctions already fixed) do not better
than some greedy or steepest-descent heuristics which need a much smaller computational effort. In this context, the intrinsic
parallelism of genetic algorithms (GAs) seems well adapted, for detecting global optima disseminated among many quasi-optimal
schedules. This paper presents several GAs for the open-shop problem. It is shown that even simple and fast versions can compete
with the best known heuristics and metaheuristics, thanks to two key-features: a population in which each individual has a distinct makespan, and a special procedure which reorders every new chromosome. Using problem-specific heuristics, it is possible to design more powerful GAs which give excellent results, even on the
hardest benchmarks of the literature: for instance, all hard open instances from Taillard are broken, except one for which
the best known solution is improved. 相似文献
7.
Laurent Lafforgue 《Inventiones Mathematicae》2002,147(1):1-241
One proves Langlands’ correspondence for GL
r
over function fields. This is a generalization of Drinfeld’s proof in the case of rank 2 : Langlands’ correspondence is realized
in ℓ-adic cohomology spaces of the modular varieties classifying rank r Drinfeld shtukas.
Oblatum 13-X-2000 & 7-VI-2001?Published online: 12 October 2001 相似文献
8.
Logarithmic SUMT limits in convex programming 总被引:1,自引:1,他引:0
The limits of a class of primal and dual solution trajectories associated with the Sequential Unconstrained Minimization Technique
(SUMT) are investigated for convex programming problems with non-unique optima. Logarithmic barrier terms are assumed. For
linear programming problems, such limits – of both primal and dual trajectories – are strongly optimal, strictly complementary,
and can be characterized as analytic centers of, loosely speaking, optimality regions. Examples are given, which show that
those results do not hold in general for convex programming problems. If the latter are weakly analytic (Bank et al. [3]),
primal trajectory limits can be characterized in analogy to the linear programming case and without assuming differentiability.
That class of programming problems contains faithfully convex, linear, and convex quadratic programming problems as strict
subsets. In the differential case, dual trajectory limits can be characterized similarly, albeit under different conditions,
one of which suffices for strict complementarity.
Received: November 13, 1997 / Accepted: February 17, 1999?Published online February 22, 2001 相似文献
9.
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
10.
An improved rounding method and semidefinite programming relaxation for graph partition 总被引:8,自引:0,他引:8
Given an undirected graph G=(V,E) with |V|=n and an integer k between 0 and n, the maximization graph partition (MAX-GP) problem is to determine a subset S⊂V of k nodes such that an objective function w(S) is maximized. The MAX-GP problem can be formulated as a binary quadratic program and it is NP-hard. Semidefinite programming
(SDP) relaxations of such quadratic programs have been used to design approximation algorithms with guaranteed performance
ratios for various MAX-GP problems. Based on several earlier results, we present an improved rounding method using an SDP
relaxation, and establish improved approximation ratios for several MAX-GP problems, including Dense-Subgraph, Max-Cut, Max-Not-Cut,
and Max-Vertex-Cover.
Received: March 10, 2000 / Accepted: July 13, 2001?Published online February 14, 2002 相似文献
11.
We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with
k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values.
Received: August 2001 / Accepted: January 2002?Published online March 27, 2002 相似文献
12.
Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions 总被引:5,自引:0,他引:5
In this paper we study primal-dual path-following algorithms for the second-order cone programming (SOCP) based on a family
of directions that is a natural extension of the Monteiro-Zhang (MZ) family for semidefinite programming. We show that the
polynomial iteration-complexity bounds of two well-known algorithms for linear programming, namely the short-step path-following
algorithm of Kojima et al. and Monteiro and Adler, and the predictor-corrector algorithm of Mizuno et al., carry over to the
context of SOCP, that is they have an O( logε-1) iteration-complexity to reduce the duality gap by a factor of ε, where n is the number of second-order cones. Since the MZ-type family studied in this paper includes an analogue of the Alizadeh,
Haeberly and Overton pure Newton direction, we establish for the first time the polynomial convergence of primal-dual algorithms
for SOCP based on this search direction.
Received: June 5, 1998 / Accepted: September 8, 1999?Published online April 20, 2000 相似文献
13.
Satoru Fujishige 《Mathematical Programming》2000,88(1):217-220
U. Faigle and W. Kern have recently extended the work of their earlier paper and of M. Queyranne, F. Spieksma and F. Tardella
and have shown that a dual greedy algorithm works for a system of linear inequalities with {:0,1}-coefficients defined in
terms of antichains of an underlying poset and a submodular function on the set of ideals of the poset under some additional
condition on the submodular function.?In this note we show that Faigle and Kern’s dual greedy polyhedra belong to a class
of submodular flow polyhedra, i.e., Faigle and Kern’s problem is a special case of the submodular flow problem that can easily
be solved by their greedy algorithm.
Received: February 1999 / Accepted: December 1999?Published online February 23, 2000 相似文献
14.
Gongyun Zhao 《Mathematical Programming》2001,90(3):507-536
An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage
stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are
studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run
in polynomial-time.
Received: August 1998 / Accepted: August 2000?Published online April 12, 2001 相似文献
15.
Krzysztof C. Kiwiel 《Mathematical Programming》2001,90(1):1-25
We study a general subgradient projection method for minimizing a quasiconvex objective subject to a convex set constraint
in a Hilbert space. Our setting is very general: the objective is only upper semicontinuous on its domain, which need not
be open, and various subdifferentials may be used. We extend previous results by proving convergence in objective values and
to the generalized solution set for classical stepsizes t
k
→0, ∑t
k
=∞, and weak or strong convergence of the iterates to a solution for {t
k
}∈ℓ2∖ℓ1 under mild regularity conditions. For bounded constraint sets and suitable stepsizes, the method finds ε-solutions with an
efficiency estimate of O(ε-2), thus being optimal in the sense of Nemirovskii.
Received: October 4, 1998 / Accepted: July 24, 2000?Published online January 17, 2001 相似文献
16.
We propose feasible descent methods for constrained minimization that do not make explicit use of the derivative of the objective
function. The methods iteratively sample the objective function value along a finite set of feasible search arcs and decrease
the sampling stepsize if an improved objective function value is not sampled. The search arcs are obtained by projecting search
direction rays onto the feasible set and the search directions are chosen such that a subset approximately generates the cone
of first-order feasible variations at the current iterate. We show that these methods have desirable convergence properties
under certain regularity assumptions on the constraints. In the case of linear constraints, the projections are redundant
and the regularity assumptions hold automatically. Numerical experience with the methods in the linearly constrained case
is reported.
Received: November 12, 1999 / Accepted: April 6, 2001?Published online October 26, 2001 相似文献
17.
Song Xu 《Mathematical Programming》2000,87(3):501-517
We propose an infeasible non-interior path-following method for nonlinear complementarity problems with uniform P-functions. This method is based on the smoothing techniques introduced by Kanzow. A key to our analysis is the introduction
of a new notion of neighborhood for the central path which is suitable for infeasible non-interior path-following methods.
By restricting the iterates in the neighborhood of the central path, we provide a systematic procedure to update the smoothing
parameter and establish the global linear convergence of this method. Some preliminary computational results are reported.
Received: March 13, 1997 / Accepted: December 17, 1999?Published online February 23, 2000 相似文献
18.
19.
In this paper, we introduce a transformation that converts a class of linear and nonlinear semidefinite programming (SDP)
problems into nonlinear optimization problems. For those problems of interest, the transformation replaces matrix-valued constraints
by vector-valued ones, hence reducing the number of constraints by an order of magnitude. The class of transformable problems
includes instances of SDP relaxations of combinatorial optimization problems with binary variables as well as other important
SDP problems. We also derive gradient formulas for the objective function of the resulting nonlinear optimization problem
and show that both function and gradient evaluations have affordable complexities that effectively exploit the sparsity of
the problem data. This transformation, together with the efficient gradient formulas, enables the solution of very large-scale
SDP problems by gradient-based nonlinear optimization techniques. In particular, we propose a first-order log-barrier method
designed for solving a class of large-scale linear SDP problems. This algorithm operates entirely within the space of the
transformed problem while still maintaining close ties with both the primal and the dual of the original SDP problem. Global
convergence of the algorithm is established under mild and reasonable assumptions.
Received: January 5, 2000 / Accepted: October 2001?Published online February 14, 2002 相似文献
20.
Self-regular functions and new search directions for linear and semidefinite optimization 总被引:11,自引:0,他引:11
In this paper, we introduce the notion of a self-regular function. Such a function is strongly convex and smooth coercive on its domain, the positive real axis. We show that any
such function induces a so-called self-regular proximity function and a corresponding search direction for primal-dual path-following
interior-point methods (IPMs) for solving linear optimization (LO) problems. It is proved that the new large-update IPMs enjoy
a polynomial ?(n
log) iteration bound, where q≥1 is the so-called barrier degree of the kernel function underlying the algorithm. The constant hidden in the ?-symbol depends
on q and the growth degree p≥1 of the kernel function. When choosing the kernel function appropriately the new large-update IPMs have a polynomial ?(lognlog) iteration bound, thus improving the currently best known bound for large-update methods by almost a factor . Our unified analysis provides also the ?(log) best known iteration bound of small-update IPMs. At each iteration, we need to solve only one linear system. An extension
of the above results to semidefinite optimization (SDO) is also presented.
Received: March 2000 / Accepted: December 2001?Published online April 12, 2002 相似文献