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Recently, the tensor complementarity problem has been investigated in the literature. In this paper, we extend a class of structured matrices to higher-order tensors; the corresponding tensor complementarity problem has a unique solution for any nonzero nonnegative vector. We discuss their relationships with semi-positive tensors and strictly semi-positive tensors. We also study the property of such a structured tensor. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. We also give two equivalent formulations of such a structured tensor. 相似文献
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In this paper, we study restricted NCP functions which may be used to reformulate the nonlinear complementarity problem as a constrained minimization problem. In particular, we consider three classes of restricted NCP functions, two of them introduced by Solodov and the other proposed in this paper. We give conditions under which a minimization problem based on a restricted NCP function enjoys favorable properties, such as equivalence between a stationary point of the minimization problem and the nonlinear complementarity problem, strict complementarity at a solution of the minimization problem, and boundedness of the level sets of the objective function. We examine these properties for three restricted NCP functions and show that the merit function based on the restricted NCP function proposed in this paper enjoys favorable properties compared with those based on the other restricted NCP functions. 相似文献
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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
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S. Park 《Journal of Optimization Theory and Applications》1997,95(2):409-417
From a general minimax inequality or an abstract lopsided saddle-point theorem, we deduce general Karamardian-type equilibrium theorems and generalized complementarity theorems. Our new results extend a number of well-known earlier works of many authors. 相似文献
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引进Stampacchia向量均衡问题与一种新的向量相补问题.用数值方法,得到它们的存在定理,并讨论Stampacchia广义向量变分不等式,向量隐相补问题与极小元问题的关系. 相似文献
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In this paper, a new notion of exceptional family of elements (EFE) for a pair of functions involved in the implicit complementarity problem (ICP) is introduced. Based upon this notion and the Leray–Schauder Alternative, a general alternative is obtained which gives more general existence theorems for the implicit complementarity problem. Finally, via the techniques of continuous selections, these existence theorems are extended to the multi-valued implicit complementarity problems (MIPS). 相似文献
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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
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The paper aims at summarizing the main results on Vector Complementarity Problems (VCP), including the existence of a solution
and the relations with Vector Variational Inequalities and Vector Optimization Problems. Particular attention will be given
to a VCP with a variable domination structure, where the ordering cone depends on the unknown variable. 相似文献
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Jie Wang Shenglong Hu Zheng-Hai Huang 《Journal of Optimization Theory and Applications》2018,176(1):120-136
In this paper, we study quadratic complementarity problems, which form a subclass of nonlinear complementarity problems with the nonlinear functions being quadratic polynomial mappings. Quadratic complementarity problems serve as an important bridge linking linear complementarity problems and nonlinear complementarity problems. Various properties on the solution set for a quadratic complementarity problem, including existence, compactness and uniqueness, are studied. Several results are established from assumptions given in terms of the comprising matrices of the underlying tensor, henceforth easily checkable. Examples are given to demonstrate that the results improve or generalize the corresponding quadratic complementarity problem counterparts of the well-known nonlinear complementarity problem theory and broaden the boundary knowledge of nonlinear complementarity problems as well. 相似文献
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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
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In this paper, we present some new smoothing techniques to solve general nonlinear complementarity problems. Under a weaker condition than monotonicity as on the original problems, we prove convergence of our methods. We also present an error estimate under a general monotonicity condition. Some numerical tests confirm the efficiency of the proposed methods. 相似文献
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Implicit Complementarity Problems in Banach Spaces 总被引:2,自引:0,他引:2
We utilize the method of multivalued fixed point in this paper to prove the existence theorems of solutions for some implicit complementarity problems in Banach spaces. 相似文献
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The main propose of this paper is devoted to studying the solvability of the generalized order tensor complementarity problem. We define two problems: the generalized order tensor complementarity problem and the vertical tensor complementarity problem and show that the former is equivalent to the latter. Using the degree theory, we present a comprehensive analysis of existence, uniqueness and stability of the solution set of a given generalized order tensor complementarity problem. 相似文献