A Note on the Paper "Linear Complementarity Problems Over Symmetric Cones: Characterization of Qb-Transformations and Existence Results"
نویسندگان
چکیده
This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). In this context, our aim is to characterize the class Qb in terms of larger classes, such as Q and R0. For this, we introduce the class F and Garćıa’s transformations. We studied them for concrete particular instances (such as second-order and semidefinite linear complementarity problems) and for specific examples (Lyapunov, Stein functions, among others). This naturally permits to establish noncoercive existence results for SCLCPs.
منابع مشابه
A full NT-step O(n) infeasible interior-point method for Cartesian P_*(k) –HLCP over symmetric cones using exponential convexity
In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...
متن کاملA full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem
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 perturbed problem, and, using the central path and feasi...
متن کاملSome Global Uniqueness and Solvability Results for Linear Complementarity Problems Over Symmetric Cones
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...
متن کاملAn improved infeasible interior-point method for symmetric cone linear complementarity problem
We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...
متن کاملInterior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones
We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in [5] depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang [17], where a vast set of conclusions concerning continuous trajectories is shown for monotone complementarity problems over t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Optimization Theory and Applications
دوره 159 شماره
صفحات -
تاریخ انتشار 2013