A new type of solution method for the generalized linear complementarity problem over a polyhedral cone

Sun, Huaijiang; Dong, Yanliang

doi:10.1007/s11633-009-0228-y

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…According to (36), we consider two cases. In the case when x ∞ ≤ 1, it is easy to see that a real-valued function f (t) = t m−1 t−1 is nondecreasing for t ≥ 0, since it is seen as a sum of some nondecreasing functions, i.e., f (t) = m−2 k=0 t k .…”

Section: Tensor Then We Have the Following Two Conclusionmentioning

confidence: 99%

“…Meanwhile, Problem G PC P(B, C, Λ, q) also includes some classical models as special cases. For example, -If A i (i = 2, • • • , m − 1) in Λ are zero tensors, then G PC P(B, C, Λ, q) (7) reduces to GT C P(B, C, A, q) (4); -If A i (i = 1, • • • , m − 2) in Λ are zero tensors, then G PC P(B, C, Λ, q) (7) reduces to the generalized linear complementarity problem over a polyhedral cone (denoted by G LC P(B, C, A, q)), which was considered by Sun et al [36]. The model is closely related to the generalized nonlinear complementarity problem over the polyhedral cone, which was extensively investigated, see, for example, Andreani et al [1], Wang et al [38], and Zhang et al [43]; -If B is the identity matrix with s = n and C is a zero matrix in the form K , then K becomes a nonnegative orthant, and so G PC P(B, C, Λ, q) (7) reduces to PC P(Λ, q) (3); -If B is the identity matrix with s = n and C is a zero matrix in the form K , and…”

Section: Introductionmentioning

confidence: 99%

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Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Shang

Yang

Tang

2021

J Optim Theory Appl

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The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all R K 0 -tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an E R K -tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature. Keywords Generalized polynomial complementarity problemCommunicated by Alexey F. Izmailov.

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Section: Tensor Then We Have the Following Two Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Shang

Yang

Tang

2021

J Optim Theory Appl

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“…Nagurney [8] presented a new theoretical framework for the quantification of strategic advantages associated with horizontal mergers through the integration of supply chain networks. For solving the variational inequalities problem, Sun and Dong [9] proposed a new type of method based on the error bound estimation.…”

Section: Literature Reviewmentioning

confidence: 99%

Supply chain network equilibrium with revenue sharing contract under demand disruptions

Yang¹,

Zhao²

2011

Int. J. Autom. Comput.

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Contract is a common and effective mechanism for supply chain coordination, which has been studied extensively in recent years. For a supply chain network model, contracts can be used to coordinate it because it is too ideal to obtain the network equilibrium state in practical market competition. In order to achieve equilibrium, we introduce revenue sharing contract into a supply chain network equilibrium model with random demand in this paper. Then, we investigate the influence on this network equilibrium state from demand disruptions caused by unexpected emergencies. When demand disruptions happen, the supply chain network equilibrium state will be broken and change to a new one, so the decision makers need to adjust the contract parameters to achieve the new coordinated state through bargaining. Finally, a numerical example with a sudden demand increase as a result of emergent event is provided for illustrative purposes.

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“…So, in this paper, we are concentrated on establishing a global error bound for the GLCP via a new type of residual function under mild conditions which can be taken as an extension of that for LCP, based on which we establish a quadratic rate of convergence for solution method without nondegenerate solution. Compared with the algorithm converges in [3,4,5], our conditions are weaker.…”

mentioning

confidence: 93%

“…The GLCP is a special case of the generalized nonlinear complementarity problem(GNCP) which was firstly considered by Andreani et al in [1], and further developed by Wang et al in [2][3][4][5], and be found applications in engineering, economics, finance, and optimization operations research [6]. For example, the GLCP plays a significant role in contact mechanics problems (such as a dynamic rigid-body model, a discretized large displacement frictional contact problem), structural mechanics problems, nonlinear obstacle problems, elastohydrodynamic lubrication problems, traffic equilibrium problems, etc.…”

mentioning

confidence: 99%