A large-step infeasible-interior-point method is proposed for solving P∗(κ)-matrix linear complementarity problems. It is new even for monotone LCP. The algorithm generates points in a large neighborhood of an infeasible central path. Each iteration requires only one matrix factorization. If the problem is solvable, then the algorithm converges from arbitrary positive starting points. The compu...

This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to co...

This paper presents a branch-and-cut algorithm for the NPhard maximum feasible subsystem problem: For a given infeasible linear inequality system, determine a feasible subsystem containing as many inequalities as possible. The complementary problem, where one has to remove as few inequalities as possible in order to make the system feasible, can be formulated as a set covering problem. The rows...

The study of the complexity of sets encompasses two complementary aims: (1) establishing-usually via explicit construction of algorithms-that sets are feasible, and (2) studying the relative complexity of sets that plausibly might be feasible but are not currently known to be feasible (such as the NP-complete sets and the PSPACE-complete sets ). For the study of the complexity of closure proper...

In this paper we investigate Multi-Objective Integer Linear Programming (MOILP) problems with unbounded feasible region and introduce recession direction for MOILP problems. Then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. Finally we present some examples with unbounded feasible region and fi...

An uncovered bargaining solution is a bargaining solution for which there exists a complete and strict relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions. J.E.L. codes: C72, D44.

One aspect of brainstorming that has received little research attention is how the brainstorming task should be presented to the group, whether as one allencompassing question or as a series of separate questions each focusing on one aspect of the task. This paper reports the results of an experiment in which groups electronically brainstormed on intact tasks (where all parts of the task were p...

In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab [1] configuration framework.