共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper is devoted to solving one of the main four-element Riemann-type boundary-value problems in classes of piecewise-bianalytic
functions with unit circumference as jump line. We prove a theorem on reduction of solving the stated problem to solving two
vector-matrix Riemann problems with respect to piecewise-analytic vector-functions. Using it, we obtain an algorithm for solving
the problem and conditions under which one can get a constructive and explicit solution in terms of Cauchy-type integrals.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 377–385, July–September, 2006. 相似文献
2.
0–1 problems are often difficult to solve. Although special purpose algorithms (exact as well as heuristic) exist for solving
particular problem classes or problem instances, there are few general purpose algorithms for solving practical-sized instances
of 0–1 problems. This paper deals with a general purpose heuristic algorithm for 0–1 problems. In this paper, we compare two
methods based on simulated annealing for solving general 0–1 integer programming problems. The two methods differe in the
scheme used for neighbourhood transitions in the simulated annealing framework. We compare the performance of the two methods
on the set partitioning problem. 相似文献
3.
Regular solutions to second-order elliptic systems on the plane are representable in terms of A-analytic functions satisfying an operator equation of the Beltrami type. We prove Carleman-type formulas for reconstruction of solutions from data on a part of the boundary of the domain. We use these formulas for solving the Cauchy problems for the system of Lame equations, the Navier–Stokes system, and the system of equations of elasticity with resilience. 相似文献
4.
Reuven Rubinstein 《Methodology and Computing in Applied Probability》2009,11(4):491-549
We present a randomized algorithm, called the cloning algorithm, for approximating the solutions of quite general NP-hard
combinatorial optimization problems, counting, rare-event estimation and uniform sampling on complex regions. Similar to the
algorithms of Diaconis–Holmes–Ross and Botev–Kroese the cloning algorithm is based on the MCMC (Gibbs) sampler equipped with
an importance sampling pdf and, as usual for randomized algorithms, it uses a sequential sampling plan to decompose a “difficult”
problem into a sequence of “easy” ones. The cloning algorithm combines the best features of the Diaconis–Holmes–Ross and the
Botev–Kroese. In addition to some other enhancements, it has a special mechanism, called the “cloning” device, which makes
the cloning algorithm, also called the Gibbs cloner fast and accurate. We believe that it is the fastest and the most accurate randomized algorithm for counting known so far.
In addition it is well suited for solving problems associated with the Boltzmann distribution, like estimating the partition
functions in an Ising model. We also present a combined version of the cloning and cross-entropy (CE) algorithms. We prove
the polynomial complexity of a particular version of the Gibbs cloner for counting. We finally present efficient numerical
results with the Gibbs cloner and the combined version, while solving quite general integer and combinatorial optimization
problems as well as counting ones, like SAT. 相似文献
5.
A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity
function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the
penalized Fischer–Burmeister function for symmetric cone complementarity problems. We show that this class of functions is
indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity
functions is coercive. 相似文献
6.
In this work, we study continuous reformulations of zero–one programming problems. We prove that, under suitable conditions,
the optimal solutions of a zero–one programming problem can be obtained by solving a specific continuous problem. 相似文献
7.
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
8.
This paper presents a new complexity result for solving multiobjective integer programming problems. We prove that encoding
the entire set of nondominated solutions of the problem in a short sum of rational functions is polynomially doable, when
the dimension of the decision space is fixed. This result extends a previous result presented in De Loera et al. (INFORMS
J. Comput. 21(1):39–48, 2009) in that there the number of the objective functions is assumed to be fixed whereas ours allows this number to vary. 相似文献
9.
Shumin Li 《Applicable analysis》2013,92(11):2287-2307
In this paper, we consider Carleman-type estimate and consider an inverse problem for second order hyperbolic systems in an anisotropic case. In the previous Part I paper, we established a Carleman-type estimate for hyperbolic systems in which the coefficient matrices satisfy suitable conditions. We apply a Carleman estimate in the previous Part I paper to an inverse source problem for second-order hyperbolic systems in an anisotropic case and prove an estimate of the Hölder type. 相似文献
10.
We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish
two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The first one allows us to
obtain a unified dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz
and Sosa (J Glob Optim 25:311–319, 2006) for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent
to Mosco’s dual problem (Mosco in J Math Anal Appl 40:202–206, 1972) when applied to a variational inequality problem. The
second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg
(Optimization 57:795–805, 2008) for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality
conditions for (GEP) and also, gap functions for (GEP), which cover the ones in Antangerel et al. (J Oper Res 24:353–371,
2007, Pac J Optim 2:667–678, 2006) for variational inequalities and standard convex equilibrium problems. These results, in
turn, when applied to DC and convex optimization problems with convex constraints (considered as special cases of (GEP)) lead
to Toland-Fenchel-Lagrange duality for DC problems in Dinh et al. (Optimization 1–20, 2008, J Convex Anal 15:235–262, 2008),
Fenchel-Lagrange and Lagrange dualities for convex problems as in Antangerel et al. (Pac J Optim 2:667–678, 2006), Bot and
Wanka (Nonlinear Anal to appear), Jeyakumar et al. (Applied Mathematics research report AMR04/8, 2004). Besides, as consequences
of the main results, we obtain some new optimality conditions for DC and convex problems. 相似文献
11.
Yu. A. Tserkovnikov 《Theoretical and Mathematical Physics》1999,118(1):85-100
We develop a scheme for constructing chains of equations for the irreducible Green's functions. The structure of the equations
allows going beyond the usual perturbation theory in solving specific problems. We obtain general relations that allow any
correlation function to be expressed through solutions of an infinite chain of equations for the irreducible functions.
Translated from Teoreticheskaya i Matematischeskaya Fizika, Vol. 118, No. 1, pp. 105–125, January, 1999. 相似文献
12.
Napsu Karmitsa Mario Tanaka Filho José Herskovits 《Journal of Optimization Theory and Applications》2011,148(3):528-549
Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas
of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper,
we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines
the traditional cutting plane method with some features of bundle methods, and the search direction calculation of feasible
direction interior point algorithm (Herskovits, J. Optim. Theory Appl. 99(1):121–146, 1998). The algorithm to be presented generates a sequence of interior points to the epigraph of the objective function. The accumulation
points of this sequence are solutions to the original problem. We prove the global convergence of the method for locally Lipschitz
continuous functions and give some preliminary results from numerical experiments. 相似文献
13.
In this paper we study problems involving the application of the Chebyshev series [1]–[4] to solve certain computational problems.
The experimental part of the work was carried out using MAPLE. Various functions of the MAPLE program for carrying out analytic
transformations, symbolic differentiation, and graphical service make it possible to give a new estimate of the possibilities
of the Chebyshev series in solving particular problems. The Chebyshev series gives an exact representation of a zero of an
analytic function. Segments of a Chebyshev series generate higher-order recursive processes. In the present paper we discuss
the theoretical foundations of this classical approach in the one-dimensional case. We give computational formulas for the
coefficients of the Chebyshev series in the multidimensional case. We consider illustrative examples. We present experimental
results of solving several optimization problems. Thirteen tables, 8 figures. Bibliography: 14 titles.
Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 5–27. 相似文献
14.
We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of
a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem
includes the covariance selection problem that can be expressed as an ℓ
1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated
as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The
method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a
local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem,
the method can terminate in O(n3/e){O(n^3/\epsilon)} iterations with an e{\epsilon}-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim
19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the
BCGD method can be efficient for large-scale covariance selection problems with constraints. 相似文献
15.
A general family of single facility continuous location–allocation problems is introduced, which includes the decreasingly
weighted ordered median problem, the single facility Weber problem with supply surplus, and Weber problems with alternative
fast transportation network. We show in this paper that the extension of the well known Weiszfeld iterative decrease method
for solving the corresponding location problems with fixed allocation yields an always convergent scheme for the location
allocation problems. In a generic way, from each starting point, the limit point will be a locally minimal solution, whereas
for each possible exceptional situation, a possible solution is indicated. Some computational results are presented, comparing
this method with an alternating location–allocation approach.
The research of the second author was partially supported by the grant of the Algerian Ministry of High Education 001BIS/PNE/ENSEIGNANTS/BELGIQUE. 相似文献
16.
We propose a new method of solving two-dimensional quasistatic problems of thermoelasticity for isotropic multilayered bodies.
The method is based on the applicaiton of generalized functions.
Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 49–52. 相似文献
17.
In this paper we consider second order scalar elliptic boundary value problems posed over three–dimensional domains and their
discretization by means of mixed Raviart–Thomas finite elements [18]. This leads to saddle point problems featuring a discrete
flux vector field as additional unknown. Following Ewing and Wang [26], the proposed solution procedure is based on splitting
the flux into divergence free components and a remainder. It leads to a variational problem involving solenoidal Raviart–Thomas
vector fields. A fast iterative solution method for this problem is presented. It exploits the representation of divergence
free vector fields as s of the –conforming finite element functions introduced by Nédélec [43]. We show that a nodal multilevel splitting of these finite
element spaces gives rise to an optimal preconditioner for the solenoidal variational problem: Duality techniques in quotient
spaces and modern algebraic multigrid theory [50, 10, 31] are the main tools for the proof.
Received November 4, 1996 / Revised version received February 2, 1998 相似文献
18.
Roberto Andreani Joaquim J. Júdice José Mario Martínez Joao Patrício 《Numerical Algorithms》2011,57(4):457-485
Interior–point algorithms are among the most efficient techniques for solving complementarity problems. In this paper, a procedure
for globalizing interior–point algorithms by using the maximum stepsize is introduced. The algorithm combines exact or inexact
interior–point and projected–gradient search techniques and employs a line–search procedure for the natural merit function
associated with the complementarity problem. For linear problems, the maximum stepsize is shown to be acceptable if the Newton
interior–point search direction is employed. Complementarity and optimization problems are discussed, for which the algorithm
is able to process by either finding a solution or showing that no solution exists. A modification of the algorithm for dealing
with infeasible linear complementarity problems is introduced which, in practice, employs only interior–point search directions.
Computational experiments on the solution of complementarity problems and convex programming problems by the new algorithm
are included. 相似文献
19.
E. G. Grits'ko 《Journal of Mathematical Sciences》1998,88(3):407-412
We propose a scheme for constructing the solution of boundary-value problems for bodies of complicated shape by applying coboundary
or boundary elements and integral transforms. We illustrate the method of applying the finite Fourier cosine transform in
solving a mixed boundary-value problem for a body having the shape of a trapezoid.
Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 97–103. 相似文献
20.
P. M. Kleniati P. Parpas B. Rustem 《Journal of Optimization Theory and Applications》2010,145(2):289-310
We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in Lasserre (SIAM J. Optim.
17(3):822–843, 2006) and Waki et al. (SIAM J. Optim. 17(1):218–248, 2006) that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series
of semidefinite relaxations that possess the same kind of sparsity. We aim at solving the former relaxations with a decomposition-based
method, which partitions the relaxations according to their sparsity pattern. The decomposition-based method that we propose
is an extension to semidefinite programming of the Benders decomposition for linear programs (Benders, Comput. Manag. Sci.
2(1):3–19, 2005). 相似文献