We are interested in finding a solution to the tensor complementarity problem with strong M-tensor, which we call M-tensor problem. propose lower dimensional linear equation approach solve that At each iteration, only system of needs be solved. The coefficient matrices systems independent iteration after finitely many iterations. show starting from zero or some nonnegative point, method generat...

The higher order predictor (43) from [1] has to be modified in the degenerate case in order for the asymptotic convergence results from Lemma 4.6 and Theorem 4.7 to hold. More precisely equation (43) should be replaced by: where = 0 , if HLCP is nondegenerate 1 , if HLCP is degenerate. (2) The computational complexity results hold for the new algorithm, with slight modifications in the proof. C...

is known as a linear complementarity problem. Under the assumption that M is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers, {(x, y) E S: x~y~ = I.* (i = 1, 2 , . . . , n) for some/~ > 0} of the feasible region S = {(x, y) >~ 0: y = Mx + q}, where L denotes the size of the input data of the problem.

This article deals with linear complementarity problems over symmetric cones. Our objective here is to characterize global uniqueness and solvability properties for linear transformations that leave the symmetric cone invariant. Specifically, we show that, for algebra automorphisms on the Lorentz space Ln and for quadratic representations on any Euclidean Jordan algebra, global uniqueness, glob...

In this paper, we consider a class of n-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix game where the utility function of every player is given by a quadratic form defined by the payoff matrix of that player. We will call such a problem the mult...

In this paper, we present an implementing weighted path following interior point algorithm for solving linear complementarity problems. Different strategies are used for its numerical implementation. An artificial variable technique is used to compute a strictly feasible starting point. An interesting comparison with the well-known Lemke’s algorithm is done.

The values of a two-player zero-sum binary discounted game are characterized by a P-matrix linear complementarity problem (LCP). Simple formulas are given to describe the data of the LCP in terms of the game graph, discount factor, and rewards. Hence it is shown that the unique sink orientation (USO) associated with this LCP coincides with the strategy valuation USO associated with the discount...

We study linear complementarity problems depending on parameters in the right-hand side and (or) in the matrix. For the case that all elements of the right-hand side are independent parameters we give a new proof for the equivalence of three diierent important local properties of the corresponding solution set map in a neighbourhood of an element of its graph. For one-and multiparametric proble...

The convergence of the Tapia indicators for infeasible{interior{point methods for solving degenerate linear complementarity problems is investigated. A new estimate of the rate of convergence of the Tapia indicators for the indices where both primal and dual variables vanish in the solution is obtained, showing that Tapia indicators for these indices converge slower than for other indices. Use ...