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61.
Georg Ch. Pflug Andrzej Ruszczyński Rüdiger Schultz 《Mathematical Methods of Operations Research》1998,47(1):39-49
Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established. 相似文献
62.
The pivot and probe algorithm for solving a linear program 总被引:1,自引:0,他引:1
In [7] we defined acandidate constraint as one which, for at least one pivot step, contains a potential pivot, discovered that most constraints are never candidate,
and devised a modification of the simplex method in which only constraints which are currently candidates are updated. In
this paper we present another way to take advantage of this fact. We begin by solving a relaxed linear program consisting
of the constraints of the original problem which are initially candidates. Its solution gives an upper bound to the value
of the original problem. We also introduce the idea of a probe, that is, a line segment joining two vectors for the primal
problem, one of which is primal feasible, and use it to identify a most violated constraint; at the same time this gives a
lower bound to the objective value of the original problem. This violated constraint is added to the relaxed problem which
is solved again, which gives a new upper bound etc. We present computational experience indicating that time savings of 50–80%
over the simplex method can be obtained by this method, which we call PAPA, the Pivot and Probe Algorithm.
This report was prepared as part of the activities of the Management Science Research Group, Carnegie-Mellon University, under
Contract No. N00014-75-C-0621 NR 047-048 with the U.S. Office of Naval Research. Reproduction in whole or part is permitted
for any purpose of the U.S. Government. 相似文献
63.
This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems. 相似文献
64.
Sven Erlander 《Mathematical Programming》1981,21(1):137-151
This paper treats entropy constrained linear programs from modelling as well as computational aspects. The optimal solutions to linear programs with one additional entropy constraint are expressed in terms of Lagrange-multipliers. Conditions for uniqueness are given. Sensitivity and duality are studied. The Newton—Kantorovich method is used to obtain a locally convergent iterative procedure. Related problems based on maximum entropy or minimum information are discussed. 相似文献
65.
Alfonso Reinoza 《Mathematical Programming》1985,31(3):307-320
Global Newton methods for computing solutions of nonlinear systems of equations have recently received a great deal of attention.
By using the theory of generalized equations, a homotopy method is proposed to solve problems arising in complementarity and
mathematical programming, as well as in variational inequalities. We introduce the concepts of generalized homotopies and
regular values, characterize the solution sets of such generalized homotopies and prove, under boundary conditions similar
to Smale’s [10], the existence of a homotopy path which contains an odd number of solutions to the problem. We related our
homotopy path to the Newton method for generalized equations developed by Josephy [3]. An interpretation of our results for
the nonlinear programming problem will be given. 相似文献
66.
We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point
Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions
are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved
in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges
to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting
one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a
modification of cutting plane algorithms so as to make finite convergence more readily implementable. 相似文献
67.
Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this
class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied
by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained
by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or
equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty.
Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.
This research was supported by the Air Force Office of Scientific Research Grant AFOSR-83-0234 相似文献
68.
John R. Birge 《Mathematical Programming》1985,31(1):25-41
Stochastic linear programs become extremely large and complex as additional uncertainties and possible future outcomes are
included in their formulation. Row and column aggregation can significantly reduce this complexity, but the solutions of the
aggregated problem only provide an approximation of the true solution. In this paper, error bounds on the value of the optimal
solution of the original problem are obtained from the solution of the aggregated problem. These bounds apply for aggregation
of both random variables and time periods. 相似文献
69.
For a solvable monotone complementarity problem we show that each feasible point which is not a solution of the problem provides simple numerical bounds for some or all components of all solution vectors. Consequently for a solvable differentiable convex program each primal-dual feasible point which is not optimal provides simple bounds for some or all components of all primal-dual solution vectors. We also give an existence result and simple bounds for solutions of monotone compementarity problems satisfying a new, distributed constraint qualification. This result carries over to a simple existence and boundedness result for differentiable convex programs satisfying a similar constraint qualification.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based on work sponsored by National Science Foundation Grants MCS-8200632 and MCS-8102684. 相似文献
70.
Uwe H. Suhl 《Mathematical Programming》1985,32(2):165-182
We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented. 相似文献