Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

Demonstrating compliance with the applicable regulations for the Waste Isolation Pilot Plant (WIPP) requires an assessment of the Iong-term performance of the disposal system. Scenario development is one starting point of this assessment, and generates inqui~ about the present state and fiture evolution of the disposal system. Scenario development consists of four tasks: (i) identi&ing and clas...

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

The principle of complementarity in interpersonal theory states that an actor's behavior tends to "pull, elicit, invite, or evoke" responses from interaction partners who are similar in affiliation (i.e., warmth vs. hostility) and opposite in control (i.e., dominance vs. submissiveness). Furthermore, complementary interactions are proposed to evoke less negative affect and promote greater relat...

A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization andm backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large (N− ∞) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily feasible, starti...

People’s numeric probability estimates for 2 mutually exclusive and exhaustive events commonly sum to 1.0, which seems to indicate the full complementarity of subjective certainty in the 2 events (i.e., increases in certainty for one event are accompanied by decreases in certainty for the other). In this article, however, a distinction is made between the additivity of probability estimates and...

The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates complementarity and substitutability to a Blackwell-comparison of two auxiliary signals. In a special setting with a binary state space...