In this paper, we introduce a new subclass of H-matrices named extendedSDD dagger(1)(for shortly,ESDD dagger(1)) matrices, discuss the relationships among ESDD dagger(1 )matrices and other subclasses of H-matrices. Ba...
详细信息
In this paper, we introduce a new subclass of H-matrices named extendedSDD dagger(1)(for shortly,ESDD dagger(1)) matrices, discuss the relationships among ESDD dagger(1 )matrices and other subclasses of H-matrices. Based on the properties of ESDD dagger(1 )matrices, infinity norm upper bounds for the inverse ofESDD dagger 1matrices are presented. As an application, error bound for linear complementarity problems of ESDD dagger(1 )matrices is provided. Numerical examples show that the obtained results are better than some existing bounds.
An equivalence is demonstrated between solving a linearcomplementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple object...
详细信息
An equivalence is demonstrated between solving a linearcomplementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple objective programming based approach to solving linear complementarity problems is presented. Results on existence, uniqueness and computational complexity are included.
This paper studies the class INS of all realn × n matricesM for which the linearcomplementarity problem (q, M) has exactlyk solutions—k depending only onM—for all realn-vectorsq interior to the coneK(M) of vec...
详细信息
This paper studies the class INS of all realn × n matricesM for which the linearcomplementarity problem (q, M) has exactlyk solutions—k depending only onM—for all realn-vectorsq interior to the coneK(M) of vectors for which (q, M) has any solution at all. This generalizes the results in Cottle and Stone (1983) which deal with the subclassU in INS wherek equals one.
We study uncertain linear complementarity problems (LCPs), that is, problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization...
详细信息
We study uncertain linear complementarity problems (LCPs), that is, problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon Krebs and Schmidt (2020). There, we studied Gamma-robustified LCPs for l(1)- and box-uncertainty sets, whereas we now focus on ellipsoidal uncertainty sets. For uncertainty in q or M, we derive conditions for the tractability of the robust counterparts. For these counterparts, we also give conditions for the existence and uniqueness of their solutions. Finally, a case study for the uncertain traffic equilibrium problem is considered, which illustrates the effects of the values of Gamma on the feasibility and quality of the respective robustified solutions.
In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving P-*(kappa)-linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically con...
详细信息
In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving P-*(kappa)-linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, O ((1 + 4 kappa)root n log n/epsilon), which matches the currently best known iteration bound for P-*(kappa)-linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.
The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer linear Algebra Appl 17: 917-933, 2010). This algorithm is parameter dependent, and previous studie...
详细信息
The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer linear Algebra Appl 17: 917-933, 2010). This algorithm is parameter dependent, and previous studies mainly focus on giving the convergence interval of the iteration parameter. Yet the specific selection approach of the optimal parameter has not been systematically studied due to the nonlinearity of the algorithm. In this work, we first propose a novel and simple strategy for obtaining the optimal parameter of the MMS algorithm by merely solving two quadratic equations in each iteration. Further, we figure out the interval of optimal parameter which is iteration independent and give a practical choice of optimal parameter to avoid iteration-based computations. Compared with the experimental optimal parameter, the numerical results from three problems, including the Signorini problem of the Laplacian, show the feasibility, effectiveness and efficiency of the proposed strategy.
Recently, some error bounds for the linearcomplementarity problem with a weakly chained diagonally dominant B-matrix have been given under certain conditions. In this paper we provide a new and even optimal error bou...
详细信息
Recently, some error bounds for the linearcomplementarity problem with a weakly chained diagonally dominant B-matrix have been given under certain conditions. In this paper we provide a new and even optimal error bound for such linear complementarity problems under weaker conditions than those there, greatly improving the existing ones. Some numerical examples are performed to illustrate the sharpness and optimality of our new bound. (C) 2019 Elsevier Inc. All rights reserved.
Based on a well-known reformulation of the linearcomplementarity problem (LCP) as a nondifferentiable system of nonlinear equations, a Newton-type method will be described for the solution of LCPs. Under certain assu...
详细信息
Based on a well-known reformulation of the linearcomplementarity problem (LCP) as a nondifferentiable system of nonlinear equations, a Newton-type method will be described for the solution of LCPs. Under certain assumptions, it will be shown that this method has a finite termination property, i.e., if an iterate is sufficiently close to a solution of LCP, the method finds this solution in one step. This result will be applied to a recently proposed algorithm by Harker and Pang in order to prove that their algorithm also has the finite termination property.
In this paper, we establish some existence results for linear complementarity problems on closed convex cones under generalized monotonicity assumptions.
In this paper, we establish some existence results for linear complementarity problems on closed convex cones under generalized monotonicity assumptions.
New error bounds involving a parameter for linear complementarity problems are presented when the involved matrices are B-pi(R)-matrices, and the optimal values of these error bounds are determined completely by using...
详细信息
New error bounds involving a parameter for linear complementarity problems are presented when the involved matrices are B-pi(R)-matrices, and the optimal values of these error bounds are determined completely by using the monotonicity of functions of this parameter. It is shown that the optimal error bounds are sharper than that provided by Garcia-Esnaola and Pena (Calcolo 54(3): 813-822, 2017) under certain assumptions.
暂无评论