共查询到20条相似文献,搜索用时 31 毫秒
1.
Xun-Hua Gong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3598-3612
In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems. 相似文献
2.
Ouayl Chadli Qamrul Hasan Ansari Suliman Al-Homidan 《Journal of Optimization Theory and Applications》2017,172(3):726-758
The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied. 相似文献
3.
In this paper, we study the generalized vector equilibrium problems in real Hausdorff topological vector space settings. The concepts of weak solutions and strong solutions are introduced. Several new results of existence for the weak solutions and strong solutions of generalized vector equilibrium problems are derived. The new results extend and modify various existence theorems for similar problems. 相似文献
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5.
A. M. Denisov 《Computational Mathematics and Mathematical Physics》2013,53(5):580-587
Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation. 相似文献
6.
本文讨论了一类具奇异右端项的伪抛物方程的初边值问题的摄动,证明了摄动问题广义解的存在性及极限性态,并得到了当ε趋于零时,摄动问题的解在一定意义下收敛于原问题的解. 相似文献
7.
S. E. Kholodovskiĭ 《Computational Mathematics and Mathematical Physics》2007,47(9):1489-1495
An efficient method of construction of solutions to a set of boundary value problems with additional interface conditions, more complicated boundary conditions, and so on on the basis of known solutions to classical boundary value problems is proposed. The method is based on the representation of solutions to classical and more complicated problems in the form of expansions into Fourier series with subsequent reduction of one series to the other. As a result, formulas directly expressing solutions to more complicated problems in terms of solutions to classical problems are obtained. On the basis of the well-known solution to the Dirichlet problem on a half plane, solutions to boundary value problems with interface conditions (including generalized conditions of the type of a crack and a screen) on intersecting straight lines for boundary conditions of the first and the third kind are obtained. 相似文献
8.
This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved. 相似文献
9.
In this paper we examine non-convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty-immunized) global solutions of classes of non-convex quadratic problems. Firstly, we derive robust solvability results for quadratic inequality systems under parameter uncertainty. Consequently, we obtain characterizations of robust solutions for uncertain homogeneous quadratic problems, including uncertain concave quadratic minimization problems and weighted least squares. Using homogenization, we also derive characterizations of robust solutions for non-homogeneous quadratic problems. 相似文献
10.
In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws. 相似文献
11.
Guochun Wen 《中国科学A辑(英文版)》1999,42(7):681-690
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second
order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The
uniqueness theorem of solutions for the above problems and somea priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem,
the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding
theorems in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
12.
The studies of systems of variational inclusions problems and variational disclusions problems with applications 总被引:1,自引:0,他引:1
In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems. 相似文献
13.
OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE 总被引:1,自引:0,他引:1
闻国棒 《数学物理学报(B辑英文版)》2008,28(3):604-612
The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. 相似文献
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Ravi P Agarwal 《Journal of Mathematical Analysis and Applications》1982,89(2):628-638
This paper presents a method for obtaining closed form solutions to serial and nonserial dynamic programming problems with quadratic stage returns and linear transitions. Global parametric optimum solutions can be obtained regardless of the convexity of the stage returns. The closed form solutions are developed for linear, convex, and nonconvex quadratic returns, as well as the procedure for recursively solving each stage of the problem. Dynamic programming is a mathematical optimization technique which is especially powerful for certain types of problems. This paper presents a procedure for obtaining analytical solutions to a class of dynamic programming problems. In addition, the procedure has been programmed on the computer to facilitate the solution of large problems. 相似文献
16.
《European Journal of Operational Research》2005,162(3):584-601
Comparison of solutions in combinatorial problems is often based on an additive cost function inducing a complete order on solutions. We investigate here a generalization of the problem, where preferences take the form of a quasi-transitive binary relation defined on the solutions space. We first propose preference-based search algorithms for two classical combinatorial problems, namely the preferred spanning trees problem (a generalization of the minimum spanning tree problem) and the preferred paths problem (a generalization of the shortest path problem). Then, we introduce a very useful axiom for preference relations called independence. Using this axiom, we establish admissibility results concerning our preference-based search algorithms. Finally, we address the problem of dealing with non-independent preference relations and provide different possible solutions for different particular problems (e.g. lower approximation of the set of preferred solutions for multicriteria spanning trees problems, or relaxation of the independence axiom for interval-valued preferred path problems). 相似文献
17.
运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性.获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件.丰富了一阶泛函微分方程解的存在性理论. 相似文献
18.
本文中,我们首先给出了一类混合似变分不等式问题.接着,在Banach空间中研究了它的解的存在性和唯一性.最后,讨论了混合似变分不等式问题的扰动问题,并证明了扰动问题的解的存在唯一性定理. 相似文献
19.
Constrained shortest path problems have many applications in areas like network routing, investments planning and project evaluation as well as in some classical combinatorial problems with high duality gaps where even obtaining feasible solutions is a difficult task in general.We present in this paper a systematic method for obtaining good feasible solutions to hard (doubly constrained) shortest path problems. The algorithm is based essentially on the concept of efficient solutions which can be obtained via parametric shortest path calculations. The computational results obtained show that the approach proposed here leads to optimal or very good near optimal solutions for all the problems studied.From a theoretical point of view, the most important contribution of the paper is the statement of a pseudopolynomial algorithm for generating the efficient solutions and, more generally, for solving the parametric shortest path problem. 相似文献
20.
高阶微分积分方程的单调迭代法及其应用 总被引:1,自引:0,他引:1
首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果. 相似文献