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41.
Guanglu Zhou Kim-Chuan Toh Gongyun Zhao 《Computational Optimization and Applications》2004,27(3):269-283
Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a P
* LCP and has a solution. Moreover, when the problem is a monotone LCP and has a solution, we prove that the convergence rate is globally linear and it achieves `-feasibility and `-complementarity in at most O(n
2 ln(1/`)) iterations with a properly chosen starting point. 相似文献
42.
Quasi-P*-maps and P(, , )-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P*-maps as special cases. It is of interest that the class of quasi-P*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P*-map or P(, , )-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems. 相似文献
43.
Zhe-ming Wang 《计算数学(英文版)》2001,(2)
1. IlltroductionAn LCP is normally for finding vectors x, s E Wu such that:where q E aam and M E Rrsxn. An LCP is called monotonic if M is positive semi-definite. Inthis paperg M is assumed to be a P*(K)--matrir[6][9] i.e. for a K 2 0, M satisfies:for any u E ac. Obviouslys positive semi-definite matrix is a p*(0)-matrix. It wajs proved in[10] that M is a P*(K)--matrix if f M is a sufficient[1].Based on Dikin's approach, Monteiro and Adler proposed in [81 an affine scaling algorith… 相似文献
44.
In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an
H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C
1-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our
results. We present also a result on the global convergence of a derivative-free descent algorithm for solving the nonlinear
complementarity problem.
The first author is deeply indebted to Professor M. Seetharama Gowda for his numerous helpful suggestions and encouragement.
Special thanks to Professor J.-P. Crouzeix and an anonymous referees for their constructive suggestions which led to numerous
improvements in the paper. The research of the first author was supported in part by the Natural Sciences and Engineering
Research Council of Canada and Scholar Activity Grant of Thompson Rivers University. The research of the second author was
supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
45.
This paper presents an infeasible-interior-point algorithm for a class of nonmonotone complementarity problems, and analyses
its convergence and computational complexity. The results indicate that the proposed algorithm is a polynomial-time one. 相似文献
46.
We correct an error in the statement of Theorem 8 in [1].
Received: January 3, 2001 / Accepted: February 26, 2001?Published online May 18, 2001 相似文献
47.
Sensitivity analysis for variational inequalities 总被引:13,自引:0,他引:13
R. L. Tobin 《Journal of Optimization Theory and Applications》1986,48(1):191-204
Sensitivity analysis results for variational inequalities are presented which give conditions for existence and equations for calculating the derivatives of solution variables with respect to perturbation parameters. The perturbations are of both the variational inequality function and the feasible region. Results for the special case of nonlinear complementarity are also presented. A numerical example demonstrates the results for variational inequalities.The author is indebted to A. V. Fiacco for many valuable suggestions and comments. This work was supported in part by funding from the Economic Regulatory Administration, US Department of Energy, under Contract No. W31109ENG38. 相似文献
48.
Z. Wang 《BIT Numerical Mathematics》2008,48(4):799-819
We present a method for solving a class of box constrained variational inequality problems. The method makes use of a procedure
for identifying some components of the solution by bounding it with an interval vector. It is shown that the method computes
an approximate solution of the variational inequality problem by solving at most n reduced systems of equations, where n is the dimension of the problem. Among those systems, only the one of the smallest dimension has to be solved with high accuracy.
The others are solved merely to identify some components of the solution, and so the computation can be done under a very
mild requirement of accuracy. Numerical results are presented for the obstacle problem, to illustrate the efficiency of the
method.
AMS subject classification (2000) 90C33, 65G30, 65K10 相似文献
49.
A new simplicial variable dimension restart algorithm is introduced to solve the nonlinear complementarity problem on the
product spaceS of unit simplices. The triangulation which underlies the algorithm differs from the triangulations ofS used thus far. Moreover, the number of rays along which the algorithm can leave the arbitrarily chosen starting point is
much larger. More precisely, there is a ray leading from the starting point to each vertex ofS. In caseS is the product ofn one-dimensional unit simplices the alogrithm is similar to the octahedral algorithm onR
n
having 2
n
rays. Also, the accuracy of an approximate solution in the terminal simplex of the algorithm is in general better than for
the other algorithms onS. Computational results will show that the number of iterations for the new algorithm is much less. The examples concern the
computation of equilibria in noncooperative games, exchange economies and trade models.
This author is financially supported by the Netherlands Organisation for the Advancement of Pure Research (ZWO), Grant 46-98.
This research is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply” which has been approved by the
Netherlands ministry of education and sciences. 相似文献
50.
In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish
the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system.
The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the
problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of
the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly
applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and
that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge,
such properties have not appeared in the existing literature for smoothing-type algorithms.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10571134), the Natural Science
Foundation of Tianjin (Grant No. 07JCYBJC05200), and the Scientific Research Foundation for the Returned Overseas Chinese
Scholars, State Education Ministry. 相似文献