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121.
First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems 总被引:2,自引:0,他引:2
First-order and second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The necessary conditions are immediate generalizations of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as illustrated by a counterexample. Here, to go from finite to infinite dimensions, causes an essential change in the proof-techniques and the results. We present modified sufficient conditions of first-order and of second-order which are based on a strengthening of the usual assumptions on the derivative of the objective function and on the second derivative of the Lagrangian. 相似文献
122.
基于分子、分母皆线性的两点有理逼近,本文对于非线性规划提出了序列有理规划SRP方法,按两种情况进行了研究。第一种为SRP-L方法,将原问题化为等效的LP问题求解;第二种为SRP-Q方法,将原问题化为等效的QP问题求解。本文的工作说明,两点有理逼近函数对于改进优化方法是有益的。 相似文献
123.
《Operations Research Letters》2023,51(1):67-71
Let us consider a network flow respecting arc capacities and flow conservation constraints. The flow degree of a node is sum of the flow entering and leaving it. We study the problem of determining a flow that minimizes the maximum flow degree of a node. We show how to solve it in strongly polynomial time with linear programming. 相似文献
124.
125.
Laureano F. Escudero Araceli Garín María Merino Gloria Pérez 《Computational Management Science》2009,6(3):307-327
We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring
with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered
to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic
mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic
Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix
Coordination approach for the multistage 0–1 program solving is proposed. Some computational experience is reported.
相似文献
126.
Yongpei Guan Shabbir Ahmed George L. Nemhauser Andrew J. Miller 《Mathematical Programming》2006,105(1):55-84
This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under
uncertainty. We show that the classical (ℓ,S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend
the (ℓ,S) inequalities to a general class of valid inequalities, called the inequalities, and we establish necessary and sufficient conditions which guarantee that the inequalities are facet-defining. A separation heuristic for inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness
of the inequalities as cuts.
This research has been supported in part by the National Science Foundation under Award number DMII-0121495. 相似文献
127.
Adam M. Oberman & Yuanlong Ruan 《计算数学(英文版)》2020,38(6):933-951
We compute and visualize solutions to the Optimal Transportation (OT) problem for
a wide class of cost functions. The standard linear programming (LP) discretization of
the continuous problem becomes intractable for moderate grid sizes. A grid refinement
method results in a linear cost algorithm. Weak convergence of solutions is established and
barycentric projection of transference plans is used to improve the accuracy of solutions.
Optimal maps between nonconvex domains, partial OT free boundaries, and high accuracy
barycenters are presented. 相似文献
128.
《Optimization》2012,61(4):429-451
In this paper it is shown that a modified Gauss-Seidel-Algorithm with exclusion of suboptimai actions can be used for approximative solving a continuously discounted Semi-Markovian decision problem. Moreover it is proved that the overrelaxation factor of the algorithm introduced in [5] can be improved. If the sojourn times are constant and the overrelaxation factor is independent of states and actions one obtains results of Reetz [6,7] for (discrete) discounted Markovian decision problems. Finally, an example illustrates this method including exclusion of suboptimai actions 相似文献
129.
《Optimization》2012,61(1-2):181-192
In this paper we examine an N-stage stochastic decision model with a recursive reward structure whose state and action spaces are standard Borel ones. The central results relate to the validity of the optimality equations and to the sufficiency of deterministic strategies. The results expand statements known for classical dynamic programming problems with additive total rewards to a wide class of recursive reward functions under certain monotonicity and continuity assumptions. The existence of an expected utility representation of the total rewards is generally not presupposed 相似文献
130.
Karla Leigh Hoffman 《Mathematical Programming》1981,20(1):22-32
A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region. The algorithm does not involve cuts of the feasible region, requires only simplex pivot operations and univariate search computations to be performed, allows the objective function to be lower semicontinuous and nonseparable, and is guaranteed to converge to the global solution. Computational aspects of the algorithm are discussed. 相似文献