In this paper we first present a mathematical programming problem, the Extended Linear Complementarity Problem (ELCP). Next we discuss how the ELCP can be used to solve some basic problems in the system theory for a class of discrete event systems that can be modeled using the max-plus algebra, which has maximization and addition as basic operations. Finally we show that the ELCP also appears i...

The strict feasibility plays an important role in the development of theory and algorithms of complementarity problems. In this paper, we establish su cient conditions to ensure the strict feasibility of a nonlinear complementarity problem. Our analysis method, based on a newly introduced concept of -exceptional sequence, can be viewed as a uni ed approach for proving the existence of a strictl...

The mixed complementarity problem can be reformulated as a nonsmooth equation by using the median operator. In this paper, we rst study some useful properties of this reformulation and then derive the Chen-Harker-Kanzow-Smale smoothing function for the mixed complementarity problem. On the basis of this smoothing function, we present a smoothing Newton method for solving the mixed complementari...

A unified formulation as well as numerical approach is presented both for the twoand three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear Complementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by the bilinear functions and the se...

A unified formulation and a numerical approach are presented for twoand three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear Complementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by bilinear functions and second-order cone const...

A new formulation is presented for the three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a second-order cone linear complementarity problem is formulated, which consists of complementarity conditions defined by bilinear functions and second-order cone constraints. The equilibrium configurations are...

Sustainability assessments bring together different perspectives that pertain to sustainability to produce overall assessments, and a wealth of approaches and tools have been developed in the past decades. However, two major problems remain. The problem of integration concerns the surplus of possibilities for integration; different tools produce different assessments. The problem of implementat...

We investigate the properties of a new merit function which allows us to reduce a nonlinear complementarity problem to an unconstrained global minimization one. Assuming that the complementarity problem is deened by a P 0-function we prove that every stationary point of the unconstrained problem is a global solution; furthermore, if the complementarity problem is deened by a uniform P-function,...