This paper investigates the Lipschitz continuity of the solution map in the settings of horizontal, vertical, and mixed linear complementarity problems. In each of these cases, we show that the solution map is (globally) Lipschitzian if and only if the solution map is single-valued. These generalize a similar result of Murthy, Parthasarathy, and Sabatini proved in the LCP setting.

Numerous grassland experiments have found evidence for a complementarity effect, an increase in productivity with higher plant species richness due to niche partitioning. However, empirical tests of complementarity in natural forests are rare. We conducted a spatially explicit analysis of 518 433 growth records for 274 species from a 50-ha tropical forest plot to test neighborhood complementari...

Robust Solution of Mixed Complementarity Problems Steven P Dirkse Under the Supervision of Associate Professor Michael C Ferris at the University of Wisconsin Madison This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem or MCP The MCP formulation is useful for expressing systems of nonlinear inequalities and equations the complementarity al...

The nonlinear complementarity problem is cast as an unconstrained minimization problem that is obtained from an augmented Lagrangian formulation. The dimensionality of the unconstrained problem is the same as that of the original problem, and the penalty parameter need only be greater than one. Another feature of the unconstrained problem is that it has global minima of zero at precisely all th...

We discuss recent advances in mathematical programs with equilibrium constraints (MPECs). We describe the challenges posed by these problems and the current algorithmic solutions. We emphasize in particular the use of the elastic mode approach. We also present initial investigations in applications of MPECs to control problems. Ceywords: Complementarity Constraints, Equilibrium Constraints, Ela...

In this paper, we extended the result about the error estimation for linear complementarity problem to the extended linear complementarity problem (ELCP) in management equilibrium modeling. More precisely, we first present that the level set of a computable residual function is bounded, and give error estimation in level set. Based on this, we use this residual function to establish a global er...

We introduce the new concept of d-orientation sequence for continuous functions. It is shown that if there does not exist a d-orientation sequence for a continuous function, then the corresponding complementarity problem (CP) has a solution. We believe that such a result characterizes an intrinsic property of CPs. As the concept of ``exceptional family of elements'', the notion of ``d-orientati...

Robert Carson's principle of complementarity asserts that the behavioral styles of interaction partners tend to complement each other by encouraging individuals to act opposite in terms of dominance and similar in terms of warmth. The principles of complementarity further hypothesize that as relationships progress through multiple interactions, the behavioral styles of its members will be alter...

We propose an interior-point algorithm based on an elastic formulation of the `1penalty merit function for mathematical programs with complementarity constraints. The salient feature of our method is that it requires no prior knowledge of which constraints, if any, are complementarity constraints. Remarkably, the method allows for a unified treatment of both general, unstructured, degenerate pr...