Linear Complementarity Systems
نویسندگان
چکیده
We introduce a new class of dynamical systems that we call "linear complementarity systerns". The evolution of these systems typically consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the Linear Complementarity Problem of mathematical programming. The framework we describe is suitable for certain situations in which both differential equations and inequalities playa role, for instance in mechanics, electrical networks, and dynamic optimization. We present a precise definition of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions.
منابع مشابه
An infeasible interior-point method for the $P*$-matrix linear complementarity problem based on a trigonometric kernel function with full-Newton step
An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...
متن کاملAn interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
In this paper, an interior-point algorithm for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...
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 کاملImproved infeasible-interior-point algorithm for linear complementarity problems
We present a modified version of the infeasible-interior- We present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545--561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which tar...
متن کاملA Quadratically Convergent Interior-Point Algorithm for the P*(κ)-Matrix Horizontal Linear Complementarity Problem
In this paper, we present a new path-following interior-point algorithm for -horizontal linear complementarity problems (HLCPs). The algorithm uses only full-Newton steps which has the advantage that no line searchs are needed. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue.
متن کاملThe extended linear complementarity problem and linear complementary-slackness systems
The extended linear complementarity problem and linear complementary-slackness systems * B. De Schutter If you want to cite this report, please use the following reference instead: B. De Schutter, " The extended linear complementarity problem and linear complementary-slackness systems, "
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:
- SIAM Journal of Applied Mathematics
دوره 60 شماره
صفحات -
تاریخ انتشار 2000