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K. Bergstresser A. Charnes P. L. Yu 《Journal of Optimization Theory and Applications》1976,18(1):3-13
The concepts of domination structures and nondominated solutions are important in tackling multicriteria decision problems. We relax Yu's requirement that the domination structure at each point of the criteria space be a convex cone (Ref. 1) and give results concerning the set of nondominated solutions for the case where the domination structure at each point is a convex set. A practical necessity for such a generalization is discussed. We also present conditions under which a locally nondominated solution is also a globally nondominated solution. 相似文献
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S. X. Li 《Journal of Optimization Theory and Applications》1996,88(1):197-208
In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associated with dominance cones via the assumption of the quasiconcavity of the objectives. Necessary as well as sufficient conditions for such quasiconcave multiobjective programming problems are obtained.The author is indebted to one of the referees for detailed constructive comments and suggestions. Thanks are also due to the late Professor Abraham Charnes, University of Texas at Austin, and Professor Zhimin Huang, Adelphi University. 相似文献
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We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C
1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case. 相似文献
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The concepts of domination structures and nondominated solutions in multiple criteria decision problems, which were introduced by Yu, enable us to tackle general situations in which there exists information concerning the decision maker's preferences.In many of the multiple criteria decision problems the underlying domination structures are not known precisely but only fuzzily determined. Yu primarily works with the case where the domination structure at each point is a convex cone. As a result, there exists a sharp borderline dividing all solutions into nondominated solutions and the others.This paper fuzzifies the concepts of domination structures and nondominated solutions to allow them to be applied to a larger class of the multiple criteria decision problems mentioned above. Introducing the concepts of fuzzy convex cones and fuzzy polar cones, it is shown how some of the main results obtained by Yu are extended. 相似文献
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Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem
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A scheduling problem is generally to order the jobs such that a certain objective function f(π) is minimized. For some classical scheduling problems, only sufficient conditions of optimal solutions are concerned in the literature. In this paper, we study the necessary and sufficient conditions by means of the concept of critical ordering (critical jobs and their relations). These results are meaningful in recognition and characterization of optimal solutions of scheduling problems. 相似文献
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陈仕洲 《纯粹数学与应用数学》2002,18(4):374-378
给出了任意阶中立型微分方程(x(t)-p(t)g(x(τ(t)))^(n) ∫α^βt(t,ξ,x(g1(t,ξ)),x(g2(t,ξ)),…,x(gm(t,ξ)))dη(ξ)=0存在正解x(t)满足x(t)-p(t)g(x(τ(t)))/t^k→正常数(→∞)物条件,作为本文结果的特例,部分地解决了文[5]提出的公开问题2。 相似文献
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In this paper we consider the standard linear SDP problem, and its low rank nonlinear programming reformulation, based on
a Gramian representation of a positive semidefinite matrix. For this nonconvex quadratic problem with quadratic equality constraints,
we give necessary and sufficient conditions of global optimality expressed in terms of the Lagrangian function. 相似文献
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Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. 相似文献
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《Optimization》2012,61(4):527-537
Using a special scalarization, we give necessary optimality conditions for fractional multiobjective optimization problems. Under a generalized invexity, sufficient optimality conditions are also given. All over the article, the data are assumed to be continuous but not necessarily Lipschitz. 相似文献
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Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces 下载免费PDF全文
《Mathematische Nachrichten》2018,291(1):160-177
This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problem where either with is a smooth bounded domain or . The function ϕ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz–Sobolev spaces. 相似文献
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Luisa Fattorusso 《Czechoslovak Mathematical Journal》2008,58(1):113-129
Let Ω be a bounded open subset of ℝ
n
, n > 2. In Ω we deduce the global differentiability result
for the solutions u ∈ H
1 (Ω, ℝ
n
) of the Dirichlet problem
with controlled growth and nonlinearity q = 2.
The result was obtained by first extending the interior differentiability result near the boundary and then proving the global
differentiability result making use of a covering procedure. 相似文献
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Faiz A. Al-Khayyal 《Mathematical Programming》1991,51(1-3):247-255
We simplify a result by Mangasarian on the existence of solutions to the linear complementarity problem. The simplified condition gives a new geometric interpretation of the result. When used to characterize the matrix classesQ andQ
0, our condition suggests a finitely checkable sufficient condition forP andP
0.This work was supported in part by the Office of Naval Research under Contract No. N00014-86-K-0173, and by general research development funds provided by the Georgia Institute of Technology. 相似文献
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Jane J. Ye 《Journal of Mathematical Analysis and Applications》2005,307(1):350-369
In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient for global or local optimality under some MPEC generalized convexity assumptions. Moreover, we propose new constraint qualifications for M-stationary conditions to hold. These new constraint qualifications include piecewise MFCQ, piecewise Slater condition, MPEC weak reverse convex constraint qualification, MPEC Arrow-Hurwicz-Uzawa constraint qualification, MPEC Zangwill constraint qualification, MPEC Kuhn-Tucker constraint qualification, and MPEC Abadie constraint qualification. 相似文献
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