In this paper we develop systematically infeasible-interior-point methods of arbitrarily high order for solving horizontal linear complementarity problems that are sufficient in the sense of Cottle. Pang and Venkatesw...
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In this paper we develop systematically infeasible-interior-point methods of arbitrarily high order for solving horizontal linear complementarity problems that are sufficient in the sense of Cottle. Pang and Venkateswaran (1989). The results apply to degenerate problems and problems having no strictly complementary solution. Variants of these methods are described that eventually avoid recentering steps, and for which all components of the approximate solutions converge superlinearly at a high order, and other variants which even terminate with a solution of the complementarity problem after finitely many steps.
The theorem of Prager-Oettli for systems of linear equations is extended to linear complementarity problems. Moreover, using a result of Schaback, a roundoff-free formula for computer calculation of the obtained bound...
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The theorem of Prager-Oettli for systems of linear equations is extended to linear complementarity problems. Moreover, using a result of Schaback, a roundoff-free formula for computer calculation of the obtained bound is given such that the strictness of the bound is guaranteed in spite of roundoff errors.
In this paper, we apply the tolerance approach proposed by Wendell for sensitivity analysis in linear programs to study sensitivity analysis in linear complementarity problems. In the tolerance approach, we find the r...
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In this paper, we apply the tolerance approach proposed by Wendell for sensitivity analysis in linear programs to study sensitivity analysis in linear complementarity problems. In the tolerance approach, we find the range or the maximum tolerance within which the coefficients of the right-hand side of the problem can vary simultaneously and independently such that the solution of the original and the perturbed problems have the same index set of nonzero elements.
This paper aims to propose the new preconditioning approaches for solving linearcomplementarity problem (LCP). Some years ago, the preconditioned projected iterative methods were presented for the solution of the LCP...
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This paper aims to propose the new preconditioning approaches for solving linearcomplementarity problem (LCP). Some years ago, the preconditioned projected iterative methods were presented for the solution of the LCP, and the convergence of these methods has been analyzed. However, most of these methods are not correct, and this is because the complementarity condition of the preconditioned LCP is not always equivalent to that of the un-preconditioned original LCP. To overcome this shortcoming, we present a new strategy with a new preconditioner that ensures the solution of the same problem is correct. We also study the convergence properties of the new preconditioned iterative method for solving LCP. Finally, the new approach is illustrated with the help of a numerical example.
A certain class of linear complementarity problems that appeared in an economical study concerning self-employment is investigated. The principal findings for this class of linear complementarity problems are: (i) the...
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A certain class of linear complementarity problems that appeared in an economical study concerning self-employment is investigated. The principal findings for this class of linear complementarity problems are: (i) there is always a solution, which can be found by the Lemke algorithm;(ii) characterizations are found for solutions, some typical for all solutions, some typical for locally nonunique solutions, and some typical for locally unique solutions;(iii) a sufficient condition is found to guarantee a globally unique solution.
Some new error bounds for linear complementarity problems of H-matrices are presented based on the preconditioned technique. Numerical examples show that these bounds are better than some existing ones.
Some new error bounds for linear complementarity problems of H-matrices are presented based on the preconditioned technique. Numerical examples show that these bounds are better than some existing ones.
In this paper,a wide-neighborhood predictor-corrector feasible interiorpoint algorithm for linear complementarity problems is *** algorithm is based on using the classical affine scaling direction as a part in a corre...
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In this paper,a wide-neighborhood predictor-corrector feasible interiorpoint algorithm for linear complementarity problems is *** algorithm is based on using the classical affine scaling direction as a part in a corrector step,not in a predictor *** convergence analysis of the algorithm is shown,and it is proved that the algorithm has the polynomial complexity O(√n logε^(−1))which coincides with the best known iteration bound for this class of mathematical *** numerical results indicate the efficiency of the algorithm.
Aggregating linear complementarity problems under a general definition of constrained consistency leads to the possibility of consistent aggregation of linear and quadratic programming models and bimatrix games. Under...
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Aggregating linear complementarity problems under a general definition of constrained consistency leads to the possibility of consistent aggregation of linear and quadratic programming models and bimatrix games. Under this formulation, consistent aggregation of dual variables is also achieved. Furthermore, the existence of multiple sets of aggregation operators is discussed and illustrated with a numerical example. Constrained consistency can also be interpreted as a disaggregation rule. This aspect of the problem may be important for implementing macro (economic) policies by means of micro (economic) agents.
Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized...
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Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex-based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.
Second-order cone linear complementarity problems (SOCLCPs) have wide applications in real world, and the latest modulus method is proved to be an efficient solver. Here, inspired by the state-of-the-art modulus metho...
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Second-order cone linear complementarity problems (SOCLCPs) have wide applications in real world, and the latest modulus method is proved to be an efficient solver. Here, inspired by the state-of-the-art modulus method and Anderson acceleration (AA), we construct the Anderson accelerating preconditioned modulus (AA+PMS) approach. Theoretically, in the first stage, we utilize the Frechet-differentiability of the absolute value function in Jordan algebra to explore its new properties. On this basis, we establish the convergence theory for the PMS approach different from the previous analysis, and further discuss the selection strategy of parameters involved. In the second stage, we demonstrate the strong semi-smoothness of the absolute value function in Jordan algebra and, thus, establish the local convergence theory for the AA+PMS approach. Finally, we conduct rich numerical experiments with application to some well-structured examples, the second-order cone programming, the Signorini problem of the Laplacian and the three-dimensional frictional contact problem to verify the robustness and effectiveness of the AA+PMS approach.
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