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1.
广义多目标minmax问题的最优性条件和极大熵方法 总被引:1,自引:0,他引:1
本文讨论了广义多目标minmax问题的最优性条件。利用极大熵逼近函数,研究了广义多目标minmax;问题的逼近问题,在较弱的条件下,证明了由极大熵逼近函数导出的多目标逼近问题的临界点的任一极限点均为原广义多目标minmax问题的临界点。 相似文献
2.
In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient
solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of
the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium
problem are proved in locally convex spaces. 相似文献
3.
The simple resource allocation problem (also called the distribution of effort problem) is generalized by allowing more than one resource constraint. It is shown that the generalized problem can be reduced to the simple one if the coefficients in the objective function are all unity. In general, however, the problem seems to become much more difficult; the difficulty is evidenced by the failure of the incremental method which is valid for the simple problem, and the NP-hardness of the generalized problem. 相似文献
4.
《Optimization》2012,61(2):223-233
The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities. 相似文献
5.
A. L. Kazakov 《Siberian Mathematical Journal》2007,48(5):837-848
We consider the generalized Cauchy problem with data on two surfaces for a second-order quasilinear analytic system. The distinction of the generalized Cauchy problem from the traditional statement of the Cauchy problem is that the initial conditions for different unknown functions are given on different surfaces: for each unknown function we pose its own initial condition on its own coordinate axis. Earlier, the generalized Cauchy problem was considered in the works of C. Riquier, N. M. Gyunter, S. L. Sobolev, N. A. Lednev, V. M. Teshukov, and S. P. Bautin. In this article we construct a solution to the generalized Cauchy problem in the case when the system of partial differential equations additionally contains the values of the derivatives of the unknown functions (in particular outer derivatives) given on the coordinate axes. The last circumstance is a principal distinction of the problem in the present article from the generalized Cauchy problems studied earlier. 相似文献
6.
In this paper generalized type-I, generalized quasi type-I, generalized pseudo type-I and other related functions over cones
are defined for a vector minimization problem. Sufficient optimality conditions are studied for this problem using Clarke’s
generalized gradients. A Mond-Weir type dual is formulated and weak and strong duality results are established. 相似文献
7.
Nan-jing Huang Jun Li Donal ORegan 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3828-3840
In this paper, a class of generalized f-complementarity problems and three classes of variational inequalities are introduced in real Banach spaces, and the equivalences among them are established under certain conditions. Several coercivity conditions are introduced for the existence of solutions of the generalized f-complementarity problem. Under some suitable assumptions, it is shown that each of these coercivity conditions is equivalent to the nonemptyness and boundedness of the solution set for the generalized f-complementarity problem in infinite-dimensional Banach spaces, and even the nonemptyness and compactness of the solution set for the generalized f-complementarity problem in finite-dimensional spaces. The existence of least elements for the feasible set of the generalized f-complementarity problem is also presented under suitable conditions. 相似文献
8.
In this paper, we study the relationship among the generalized Minty vector variational-like inequality problem, generalized
Stampacchia vector variational-like inequality problem and vector optimization problem for nondifferentiable and nonconvex
functions. We also consider the weak formulations of the generalized Minty vector variational-like inequality problem and
generalized Stampacchia vector variational-like inequality problem and give some relationships between the solutions of these
problems and a weak efficient solution of the vector optimization problem. 相似文献
9.
Qamrul Hasan Ansari Mahboubeh Rezaie Jafar Zafarani 《Journal of Global Optimization》2012,53(2):271-284
In this paper, we consider different kinds of generalized vector variational-like inequality problems and a vector optimization problem. We establish some relationships between the solutions of generalized Minty vector variational-like inequality problem and an efficient solution of a vector optimization problem. We define a perturbed generalized Stampacchia vector variational-like inequality problem and discuss its relation with generalized weak Minty vector variational-like inequality problem. We establish some existence results for solutions of our generalized vector variational-like inequality problems. 相似文献
10.
The optimal control problem for systems with controlled unilateral phase constraints is considered. The definition of the generalized solutions is introduced, the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed, and the necessary optimality conditions are found. 相似文献
11.
In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievable minimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition. 相似文献
12.
G. Giorgadze 《Journal of Mathematical Sciences》2006,132(6):716-738
We discuss a number of topics concerned with certain boundary-value problems in the context of generalized analytic functions.
Solution of the classical Riemann-Hilbert problem and the linear conjugation problem for analytic functions is described in
appropriate function classes and the same scheme is applied to generalized analytic functions and vectors. In particular,
we describe solution of the Riemann-Hilbert problem for generalized analytic functions and obtain an explicit analytic presentation
of monodromy matrices in the case of generalized analytic vectors.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 15, Theory
of Functions, 2004. 相似文献
13.
Bidushi Chakraborty Sudarshan Nanda Mahendra Prasad Biswal 《Mediterranean Journal of Mathematics》2005,2(3):291-299
In this paper, generalization of a vertical block linear complementarity problem associated with two different types of matrices,
one of which is a square matrix and the other is a vertical block matrix, is proposed. The necessary and sufficient conditions
for the existence of the solution of the generalized vertical block linear complementarity problem is derived and the relationship
between the solution set of the generalized vertical block linear complementarity problem and the linear complementarity problem
is established. It is proved that the generalized vertical block linear complementarity problem has the P-property if and only if the vertical block linear complementarity problem has the P-property. 相似文献
14.
童子双 《数学的实践与认识》2009,39(14)
结合F-凸,η-不变凸及d一致不变凸的概念给出了非光滑广义(F,ρ,θ)-d一致不变凸函数;就一类在凸集C上目标函数为Lipschitz连续的带有可微不等式约束的广义分式规划,提出一个对偶,并利用在广义Kuhn-Tucker约束品性或广义Arrow-Hurwicz-Uzawa约束品性的条件下得到的最优性必要条件,证明相应的弱对偶定理、强对偶定理及严格逆对偶定理. 相似文献
15.
A. L. Kazakov 《Siberian Mathematical Journal》2006,47(2):245-257
The generalized Cauchy problem with data on three surfaces is under consideration for a quasilinear analytic system of the third order. Under some simplifying assumption, we find necessary and sufficient conditions for existence of a solution in the form of triple series in the powers of the independent variables. We obtain convenient sufficient conditions under which the data of the generalized Cauchy problem has a unique locally analytic solution. We give counterexamples demonstrating that in the case we study it is impossible to state necessary and sufficient conditions for analytic solvability of the generalized Cauchy problem. We also show that the analytic solution can fail to exist even if the generalized Cauchy problem with data on three surfaces has a formal solution since the series converge only at a sole point, the origin. 相似文献
16.
In this paper, we consider Levitin–Polyak well-posedness of parametric generalized equilibrium problems and optimization problems
with generalized equilibrium constraints. Some criteria for these types of well-posedness are derived. In particular, under
certain conditions, we show that generalized Levitin–Polyak well-posedness of a parametric generalized equilibrium problem
is equivalent to the nonemptiness and compactness of its solution set. Finally, for an optimization problem with generalized
equilibrium constraints, we also obtain that, under certain conditions, Levitin–Polyak well-posedness in the generalized sense
is equivalent to the nonemptiness and compactness of its solution set. 相似文献
17.
Rong AN Yuan LI Kai-tai LI College of Mathematics Information Science Wenzhou University Wenzhou China School of Science Xi’an Jiaotong University Xi’an China 《应用数学学报(英文版)》2011,(4)
In this paper,the fundamental solution of rotating generalized Stokes problem in R 3 is established.To obtain it,some fundamental solutions of other problems also are established,such as generalized Laplace problem,generalized Stokes problem and rotating Stokes problem. 相似文献
18.
We address a problem of vehicle routing that arises in picking up and delivering full container load from/to an intermodal terminal. The substantial cost and time savings are expected by efficient linkage between pickup and delivery tasks, if the time of tasks and the suitability of containers for cargo allow. As this problem is NP-hard, we develop a subgradient heuristic based on a Lagrangian relaxation which enables us to identify a near optimal solution. The heuristic consists of two sub-problems: the classical assignment problem and the generalized assignment problem. As generalized assignment problem is also NP-hard, we employ an efficient solution procedure for a bin packing based problem, which replaces the generalized assignment problem. The heuristic procedure is tested on a wide variety of problem examples. The test results demonstrate that the procedure developed here can efficiently solve large instances of the problem. 相似文献
19.
J. M. Peng & Y. Yuan 《计算数学(英文版)》1997,15(3):253-264
1.IntroductionThecomplementarityproblem,aspecialcaseofvariationalinequalityproblem,hasmanyapplicationsindifferentfieldssuchasmathematicalprogramming,gametheory,economics.Generally,thestandardcomplementarityproblemhasthefollowingform:y=F(x),x20,y20,(y,x)=0,(1.1)where(.,.)denotestheinnerproducts.WhenF(x)isanaffinefunctionofx,itreducestothelinearcomplementarityproblemwhichisdenotedbyLCP.Otherwisewecallitthenonlinearco7nplementaritypro6lemorsimplyNCP.Thecomplementarityproblemhajsattractedmanyr… 相似文献
20.
研究广义双随机矩阵反问题.给出广义双随机矩阵的最小二乘解,得到了解的具体表达形式.并讨论了用广义双随机矩阵构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达形式.包括算法及数值例子. 相似文献