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1.
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
2.
Recent advances in the solution of quadratic assignment problems 总被引:6,自引:0,他引:6
Kurt M. Anstreicher 《Mathematical Programming》2003,97(1-2):27-42
The quadratic assignment problem (QAP) is notoriously difficult for exact solution methods. In the past few years a number
of long-open QAPs, including those posed by Steinberg (1961), Nugent et al. (1968) and Krarup (1972) were solved to optimality
for the first time. The solution of these problems has utilized both new algorithms and novel computing structures. We describe
these developments, as well as recent work which is likely to result in the solution of even more difficult instances.
Received: February 13, 2003 / Accepted: April 22, 2003
Published online: May 28, 2003
Key Words. quadratic assignment problem – discrete optimization – branch and bound
Mathematics Subject Classification (1991): 90C27, 90C09, 90C20 相似文献
3.
We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on
a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters
to these functions: one is used to control the slope and the other controls the deviation from the exact penalty.
We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz
constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained
for non-smooth convex problems under a Slater qualification condition.
Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003
Research partially supported by CAPES, Brazil
Research partially supported by CNPq, Brazil, and CONICIT, Venezuela.
Mathematics Subject Classification (1991): 20E28, 20G40, 20C20 相似文献
4.
Mikael Rönnqvist 《Mathematical Programming》2003,97(1-2):267-284
Optimization models and methods have been used extensively in the forest industry. In this paper we describe the general
wood-flow in forestry and a variety of planning problems. These cover planning periods from a fraction of a second to more
than one hundred years. The problems are modelled using linear, integer and nonlinear models. Solution methods used depend
on the required solution time and include for example dynamic programming, LP methods, branch & bound methods, heuristics
and column generation. The importance of modelling and qualitative information is also discussed.
Received: January 15, 2003 / Accepted: April 24, 2003
Published online: May 28, 2003
Key words. Forestry – modelling – routing – transportation – production planning
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20 相似文献
5.
We review the necessary background on Corner Polyhedra and use this to show how knowledge about Corner Polyhedra and subadditive
functions translates into a great variety of cutting planes for general integer programming problems. Experiments are described
that indicate the dominance of a relatively small number of the facets of Corner Polyhedra. This has implications for their
value as cutting planes.
Received: May 24, 2001 / Accepted: August 2002
Published online: March 21, 2003
Mathematics Subject Classification (1991): 20E28, 20G40, 20C20 相似文献
6.
Yi Zhang 《Archive for Mathematical Logic》2003,42(2):153-163
We construct several forcing models in each of which there exists a maximal cofinitary group, i.e., a maximal almost disjoint
group, G≤Sym(ℕ), such that G is also a maximal almost disjoint family in Sym(ℕ). We also ask several open questions in this area in the fourth section of this paper.
Received: 25 December 2000 / Revised version: 10 December 2001 Published online: 5 November 2002
Current address:Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109. USA.e-mail: yizhang@umich.edu
The author's research on this subject was partially supported by a visiting grant from the Institute Mittag–Leffler, Royal
Academy of Science, Sweden and the grant no. 40734 of Academy of Finland.
Mathematics Subject Classification (2000): 03E35, 20A15, 20B07, 20B35 相似文献
7.
Let be a parametric variational double integral and γ ⊂ ℝ
n
be a system of several distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers
of spanned in γ by solving the Douglas problem for parametric functionals on multiply connected schlicht domains. As a by-product
we obtain a simple isoperimetric inequality for multiply connected -minimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau
problem.
Received: 19 April 2002
Mathematics Subject Classification (2000): 49J45, 49Q10, 53A07, 53A10 相似文献
8.
Via the Linking Theorem and Pseudo-index theory, we consider the existence and multiplicity of nontrivial solutions for a
class of elliptic problems in all of ℝ
N
with indefinite linear part involving resonance and non-resonance at any eigenvalue.
Received: 9 September 2002 / Revised version: 14 February 2003
Published online: 24 April 2003
Mathematics Subject Classification (2000): 35J20, 35J70 相似文献
9.
Combining search directions using gradient flows 总被引:2,自引:0,他引:2
The efficient combination of directions is a significant problem in line search methods that either use negative curvature,
or wish to include additional information such as the gradient or different approximations to the Newton direction.
In this paper we describe a new procedure to combine several of these directions within an interior-point primal-dual algorithm.
Basically, we combine in an efficient manner a modified Newton direction with the gradient of a merit function and a direction
of negative curvature, if it exists. We also show that the procedure is well-defined, and it has reasonable theoretical properties
regarding the rate of convergence of the method.
We also present numerical results from an implementation of the proposed algorithm on a set of small test problems from the
CUTE collection.
Received: November 2000 / Accepted: October 2002 Published online: February 14, 2003
Key Words. negative curvature – primal-dual methods – interior-point methods – nonconvex optimization – line searches
Mathematics Subject Classification (1991): 49M37, 65K05, 90C30 相似文献
10.
Andreas Fischer 《Mathematical Programming》2002,94(1):91-124
An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations
with the structure , where is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type . The multifunction approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear
or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution
set map of the perturbed generalized equation . Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general
and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising
from nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity
properties for these problems.
Received: November 2001 / Accepted: November 2002 Published online: December 9, 2002
Key Words. generalized equation – nonisolated solutions – Newton's method – superlinear convergence – upper Lipschitz-continuity – mixed
complementarity problem – error bounds
Mathematics Subject Classification (1991): 90C30, 65K05, 90C31, 90C33 相似文献
11.
On the capacitated vehicle routing problem 总被引:1,自引:0,他引:1
We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known
customer demands for a single commodity from a common depot at minimum transit cost. This difficult combinatorial problem
contains both the Bin Packing Problem and the Traveling Salesman Problem (TSP) as special cases and conceptually lies at the
intersection of these two well-studied problems. The capacity constraints of the integer programming formulation of this routing
model provide the link between the underlying routing and packing structures. We describe a decomposition-based separation
methodology for the capacity constraints that takes advantage of our ability to solve small instances of the TSP efficiently.
Specifically, when standard procedures fail to separate a candidate point, we attempt to decompose it into a convex combination
of TSP tours; if successful, the tours present in this decomposition are examined for violated capacity constraints; if not,
the Farkas Theorem provides a hyperplane separating the point from the TSP polytope. We present some extensions of this basic
concept and a general framework within which it can be applied to other combinatorial models. Computational results are given
for an implementation within the parallel branch, cut, and price framework SYMPHONY.
Received: October 30, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002
Key words. vehicle routing problem – integer programming – decomposition algorithm – separation algorithm – branch and cut
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20 相似文献
12.
We revise the Volume Algorithm (VA) for linear programming and relate it to bundle methods. When first introduced, VA was
presented as a subgradient-like method for solving the original problem in its dual form. In a way similar to the serious/null
steps philosophy of bundle methods, VA produces green, yellow or red steps. In order to give convergence results, we introduce
in VA a precise measure for the improvement needed to declare a green or serious step. This addition yields a revised formulation
(RVA) that is halfway between VA and a specific bundle method, that we call BVA. We analyze the convergence properties of
both RVA and BVA. Finally, we compare the performance of the modified algorithms versus VA on a set of Rectilinear Steiner
problems of various sizes and increasing complexity, derived from real world VLSI design instances.
Received: December 1999 / Accepted: September 2002 Published online: December 19, 2002
Key Words. volume algorithm – bundle methods – Steiner problems
Correspondence to: Claudia A. Sagastizábal, e-mail: sagastiz@impa.br 相似文献
13.
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
14.
François Margot 《Mathematical Programming》2002,94(1):71-90
The paper presents a branch-and-cut for solving (0, 1) integer linear programs having a large symmetry group. The group is
used for pruning the enumeration tree and for generating cuts. The cuts are non-standard, cutting integer feasible solutions
but leaving the optimal value of the problem unchanged. Pruning and cut generation are performed by backtracking procedures
using a Schreier-Sims table for representing the group. Applications to hard set covering problems and to the generation of
covering designs and error correcting codes are presented.
Received: August 2001 / Accepted: October 2002 Publication online: December 9, 2002
Key Words. branch-and-cut – isomorphism pruning – symmetry 相似文献
15.
Carmine Di Fiore Stefano Fanelli Filomena Lepore Paolo Zellini 《Numerische Mathematik》2003,94(3):479-500
Summary. In this paper a new class of quasi-Newton methods, named ℒQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra ℒ of matrices simultaneously diagonalized by a fast
unitary transform. The complexity per step of ℒQN methods is O(n log n), thereby improving considerably BFGS computational efficiency. Moreover, since ℒQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result
is obtained under suitable assumptions on f. Numerical experiences [7] confirm that ℒQN methods are particularly recommended for large scale problems.
Received December 30, 2001 / Revised version received December 20, 2001 /
Published online November 27, 2002
Mathematics Subject Classification (1991): 65K10
Correspondence to: P. Zellini 相似文献
16.
We introduce a new upper bound for the maximum-entropy sampling problem. Our bound is described as the solution of a linear
integer program. The bound depends on a partition of the underlying set of random variables. For the case in which each block
of the partition has bounded cardinality, we describe an efficient dynamic-programming algorithm to calculate the bound. For
the very special case in which the blocks have no more than two elements, we describe an efficient algorithm for calculating
the bound based on maximum-weight matching. This latter formulation has particular value for local-search procedures that
seek to find a good partition. We relate our bound to recent bounds of Hoffman, Lee and Williams. Finally, we report on the
results of some computational experiments.
Received: September 27, 2000 / Accepted: July 26, 2001 Published online: September 5, 2002
Key words. experimental design – design of experiments – entropy – maximum-entropy sampling – matching – integer program – spectral
bound – Fischer's inequality – branch-and-bound – dynamic programming
Mathematics Subject Classification (2000): 52B12, 90C10
Send offprint requests to: Jon Lee
Correspondence to: Jon Lee 相似文献
17.
Imre Patyi 《Mathematische Annalen》2003,326(3):417-441
Let X be a complex Banach space with a countable unconditional basis, Ω⊂X pseudoconvex open, G a complex Banach Lie group. We show that a Runge–type approximation hypothesis on X, G (which we also prove for G a solvable Lie group) implies that any holomorphic cocycle on Ω with values in G can be resolved holomorphically if it can be resolved continuously.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L05, 32E30, 46G20
RID="*"
ID="*" Kedves Szímuskának.
RID="*"
ID="*" To my dear Wife. 相似文献
18.
The split cuts of Cook, Kannan and Schrijver are general-purpose valid inequalities for integer programming which include a variety of other
well-known cuts as special cases. To detect violated split cuts, one has to solve the associated separation problem. The complexity of split cut separation was recently cited as an open problem by Cornuéjols & Li CL01.
In this paper we settle this question by proving strong 𝒩𝒫-completeness of separation for split cuts. As a by-product we
also show 𝒩𝒫-completeness of separation for several other classes of inequalities, including the MIR-inequalities of Nemhauser and Wolsey and some new inequalities which we call balanced split cuts and binary split cuts. We also strengthen 𝒩𝒫-completeness results of Caprara & Fischetti CF96 (for
-cuts) and Eisenbrand E99 (for Chvátal-Gomory cuts).
To compensate for this bleak picture, we also give a positive result for the Symmetric Travelling Salesman Problem. We show how to separate in polynomial time over a class of split cuts which includes all comb inequalities with a fixed handle.
Received: October 23, 2000 / Accepted: October 03, 2001 Published online: September 5, 2002
Key words. cutting planes – separation – complexity – travelling salesman problem – comb inequalities 相似文献
19.
This work is concerned with existence for a stochastic free boundary problem arising in phase transition (the Stefan two
phase problem). The existence of an invariant ergodic measure associated with the corresponding transition semigroup P(t) is also proved, together with an integration by parts formula for the generator of P(t).
Received: 20 June 2001 / Revised version: 17 June 2002 / Published online: 24 October 2002
Mathematics Subject Classification (2000): 35K35, 35R15, 60H15
Key words or phrases: Stochastic Stefan problem – Invariant measures – Wiener process – Transition semigroup – Kolmogorov operator 相似文献
20.
Stephen M. Robinson 《Mathematical Programming》2003,97(1-2):245-265
This is an expository paper about the analysis of variational conditions over sets defined in finite-dimensional spaces by
fairly smooth functions satisfying a constraint qualification. The primary focus is on results that can provide quantitative
and computable sensitivity information for particular instances of the problems under study, and our objective is to give
a personal view of the state of current knowledge in this area and of gaps in that knowledge that require future work. The
writing style is informal, in keeping with the objective of focusing the reader's attention on the basic concepts and the
relationships between them, rather than on details of the particular results themselves.
Received: December 1, 2002 / Accepted: April 25, 2003
Published online: May 28, 2003
Key words. variational condition – variational inequality – complementarity – sensitivity – stability – nondegeneracy
Mathematics Subject Classification (2000): Primary: 90C31. Secondary: 47J20, 49J40, 49J53, 90C33 相似文献