The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Yisheng Song - One of the best experts on this subject based on the ideXlab platform.
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properties of solution set of tensor Complementarity Problem
Journal of Optimization Theory and Applications, 2016Co-Authors: Yisheng SongAbstract:In this paper, a new subclass of tensors is introduced and it is proved that this class of new tensors can be defined by the feasible region of the corresponding tensor Complementarity Problem. Furthermore, the boundedness of solution set of the tensor Complementarity Problem is equivalent to the uniqueness of solution for such a Problem with zero vector. For the tensor Complementarity Problem with a strictly semi-positive tensor, we proved the global upper bounds of its solution set. In particular, such upper bounds are closely associated with the smallest Pareto eigenvalue of such a tensor.
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Tensor Complementarity Problem and Semi-positive Tensors
Journal of Optimization Theory and Applications, 2015Co-Authors: Yisheng SongAbstract:In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor Complementarity Problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor Complementarity Problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.
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properties of solution set of tensor Complementarity Problem
arXiv: Optimization and Control, 2015Co-Authors: Yisheng SongAbstract:The tensor Complementarity Problem is a specially structured nonlinear Complementarity Problem, then it has its particular and nice properties other than ones of the classical nonlinear Complementarity Problem. In this paper, it is proved that a tensor is an S-tensor if and only if the tensor Complementarity Problem is feasible, and each Q-tensor is an S-tensor. Furthermore, the boundedness of solution set of the tensor Complementarity Problem is equivalent to the uniqueness of solution for such a Problem with zero vector. For the tensor Complementarity Problem with a strictly semi-positive tensor, we proved the global upper bounds for solution of such a Problem. In particular, the upper bounds keep in close contact with the smallest Pareto $H-$($Z-$)eigenvalue.
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Tensor Complementarity Problem and Semi-positive Tensors
arXiv: Optimization and Control, 2015Co-Authors: Yisheng SongAbstract:The tensor Complementarity Problem $(\q, \mathcal{A})$ is to $$\mbox{ find } \x \in \mathbb{R}^n\mbox{ such that }\x \geq \0, \q + \mathcal{A}\x^{m-1} \geq \0, \mbox{ and }\x^\top (\q + \mathcal{A}\x^{m-1}) = 0.$$ We prove that a real tensor $\mathcal{A}$ is a (strictly) semi-positive tensor if and only if the tensor Complementarity Problem $(\q, \mathcal{A})$ has a unique solution for $\q>\0$ ($\q\geq\0$), and a symmetric real tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive. That is, for a strictly copositive symmetric tensor $\mathcal{A}$, the tensor Complementarity Problem $(\q, \mathcal{A})$ has a solution for all $\q \in \mathbb{R}^n$.
Uwe Schäfer - One of the best experts on this subject based on the ideXlab platform.
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A Linear Complementarity Problem with a P-Matrix
SIAM Review, 2004Co-Authors: Uwe SchäferAbstract:In this paper, we present an application of a linear Complementarity Problem where M is a P-matrix but, in general, is neither an H-matrix nor a positive definite matrix. This application occurs originally in [J. Rohn, Linear Algebra Appl., 126 (1989), pp. 39--78], which is less known to the LCP community. Its focus is in computing the exact interval enclosures of the components of the solution set of an interval linear system. We extend the idea such that the calculations can be done by a computer with rigorous error control.
Yiju Wang - One of the best experts on this subject based on the ideXlab platform.
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solution structures of tensor Complementarity Problem
Frontiers of Mathematics in China, 2018Co-Authors: Xueyong Wang, Haibin Chen, Yiju WangAbstract:We introduce two new types of tensors called the strictly semimonotone tensor and the range column sufficient tensor and explore their structure properties. Based on the obtained results, we make a characterization to the solution of tensor Complementarity Problem.
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further discussion on the error bound for generalized linear Complementarity Problem over a polyhedral cone
Journal of Optimization Theory and Applications, 2013Co-Authors: Hongchun Sun, Yiju WangAbstract:In this paper, we consider the global error bound for the generalized linear Complementarity Problem over a polyhedral cone (GLCP). Based on the new transformation of the Problem, we establish its global error bound under milder conditions, which improves the result obtained by Sun and Wang (2009) for GLCP by weakening the assumption.
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a smoothing inexact newton method for p 0 nonlinear Complementarity Problem
Frontiers of Mathematics in China, 2012Co-Authors: Haitao Che, Yiju WangAbstract:We first propose a new class of smoothing functions for the nonlinear Complementarity function which contains the well-known Chen-Harker-Kanzow-Smale smoothing function and Huang-Han-Chen smoothing function as special cases, and then present a smoothing inexact Newton algorithm for the P0 nonlinear Complementarity Problem. The global convergence and local superlinear convergence are established. Preliminary numerical results indicate the feasibility and efficiency of the algorithm.
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Global Error Bound Estimation for the Generalized Nonlinear Complementarity Problem over a Closed Convex Cone
Journal of Applied Mathematics, 2012Co-Authors: Hongchun Sun, Yiju WangAbstract:The global error bound estimation for the generalized nonlinear Complementarity Problem over a closed convex cone (GNCP) is considered. To obtain a global error bound for the GNCP, we first develop an equivalent reformulation of the Problem. Based on this, a global error bound for the GNCP is established. The results obtained in this paper can be taken as an extension of previously known results.
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a newton type algorithm for generalized linear Complementarity Problem over a polyhedral cone
Applied Mathematics and Computation, 2005Co-Authors: Xinzhen Zhang, Yiju WangAbstract:In this paper, the generalized linear Complementarity Problem over a polyhedral cone (GLCP) is reformulated as an unconstrained optimization, based on which we propose a Newton-type algorithm to solve it. Under certain conditions, we show that the algorithm converges globally and quadratically. Preliminary numerical experiments are also reported in this paper.
Behrouz Kheirfam - One of the best experts on this subject based on the ideXlab platform.
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a full nesterov todd step infeasible interior point algorithm for symmetric cone linear Complementarity Problem
Bulletin of The Iranian Mathematical Society, 2014Co-Authors: Behrouz Kheirfam, Nezam MahdaviamiriAbstract:A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear Complementarity Problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a per- turbed Problem, and, using the central path and feasibility steps, nds strictly feasible iterates for the next perturbed Problem. By using centering steps for the new perturbed Problem, strictly fea- sible iterates are obtained to be close enough to the central path of the new perturbed Problem. The starting point depends on two positive numbersp andd. The algorithm terminates either by nding an ϵ-solution or detecting that the symmetric cone linear Complementarity Problem has no optimal solution with vanishing duality gap satisfying a condition in terms ofp andd. The it- eration bound coincides with the best known bound for infeasible interior-point methods. Keywords: Monotone linear Complementarity Problem, interior- point algorithms, Euclidean Jordan algebra. MSC(2010): Primary: 90C33; Secondary: 90C51.
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a predictor corrector interior point algorithm for p κ horizontal linear Complementarity Problem
Numerical Algorithms, 2014Co-Authors: Behrouz KheirfamAbstract:We present a predictor-corrector path-following interior-point algorithm for P ? ( ? ) $P_*(\kappa )$ horizontal linear Complementarity Problem based on new search directions. In each iteration, the algorithm performs two kinds of steps: a predictor (damped Newton) step and a corrector (full Newton) step. The full Newton-step is generated from an algebraic reformulation of the centering equation, which defines the central path and seeks directions in a small neighborhood of the central path. While the damped Newton step is used to move in the direction of optimal solution and reduce the duality gap. We derive the complexity for the algorithm, which coincides with the best known iteration bound for P ? ( ? ) $P_*(\kappa )$ -horizontal linear Complementarity Problems.
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a new interior point algorithm based on modified nesterov todd direction for symmetric cone linear Complementarity Problem
Optimization Letters, 2014Co-Authors: Behrouz Kheirfam, Nezam MahdaviamiriAbstract:We present a new primal-dual path-following interior-point algorithm for linear Complementarity Problem over symmetric cones. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov–Todd step feasible interior-point algorithm based on the search directions, the complexity bound of the algorithm with the small update approach is the best available.
Song Wang - One of the best experts on this subject based on the ideXlab platform.
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a penalty method for a mixed nonlinear Complementarity Problem
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Chongchao Huang, Song WangAbstract:Abstract We propose a power penalty method for a mixed nonlinear Complementarity Problem (MNCP) and show that the solution to the penalty equation converges to that of the MNCP exponentially as the penalty parameter approaches infinity, provided that the mapping involved in the MNCP is both continuous and ξ -monotone. Furthermore, a convergence theorem is established when the monotonicity assumption on the mapping is removed. To demonstrate the usefulness and the convergence rates of this method, we design a non-trivial test MNCP Problem arising in shape-preserving bi-harmonic interpolation and apply our method to this test Problem. The numerical results confirm our theoretical findings.
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A power penalty approach to a Nonlinear Complementarity Problem
Operations Research Letters, 2010Co-Authors: Chongchao Huang, Song WangAbstract:We propose a novel power penalty approach to a Nonlinear Complementarity Problem (NCP) in which the NCP is approximated by a nonlinear equation containing a power penalty term. We show that the solution to the penalty equation converges to that of the NCP at an exponential rate when the function involved is continuous and @x-monotone. A higher convergence rate is also obtained when the function becomes Lipschitz continuous. Numerical results are presented to confirm the theoretical findings.
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Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation
Journal of Optimization Theory and Applications, 2006Co-Authors: Song Wang, X.q. Yang, Kok Lay TeoAbstract:In this paper, we present a power penalty function approach to the linear Complementarity Problem arising from pricing American options. The Problem is first reformulated as a variational inequality Problem; the resulting variational inequality Problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality Problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method.