Traditional super-efficiency data envelopment analysis (DEA) models rank efficient units under the assumption of constant returns to scale (CRS). However, infeasibility may occur in super-efficiency models under variable returns to scale (VRS). This paper proposes a modified VRS super-efficiency DEA model to deal with infeasibility by relaxing the convexity constraint 1, 0 1 n j j j λ = ≠ = ∑ t...

We prove that the subset sum problem ax = β x ∈ {0, 1}n (SUB) has a polynomial time computable certificate of infeasibility for all a with density at most 1/(2n), and for almost all β integer right hand sides. The certificate is branching on a hyperplane, i.e. by a methodology dual to the one explored by Lagarias and Odlyzko [6]; Frieze [3]; Furst and Kannan [4]; and Coster et. al. in [1]. We p...

This paper presents a knowledge-based method for identifying infeasible assembly operations in the context of assembly sequence planning. In addition the reasons for the infeasibility are identified and these can guide product designers towards the necessary design changes to make a preferred assembly sequence feasible, or guarantee that an assembly sequence includes a specific partial assembly...

In “An artificial-free simplex-type algorithm for general LP models” [Math. Comput. Model., 25 (1997), pp. 107–123] and “Initialization of the simplex algorithm: An artificial-free approach” [SIAM Rev., 39 (1997), pp. 736–744], Arsham presents a new Phase 1 algorithm for the simplex method of linear programming, which allegedly obviates the use of artificial variables. He claims in [SIAM Rev., ...

Algorithms for Distributed Constraint Satisfaction Problems fall into two categories: distributed complete search (DisCS) and distributed local search (DisLS). The advantage of DisCS is that it guarantees to find a solution or proves problem infeasibility. DisCS is good at solving tight problems with complex constraints, but suffers from false commitments early in the search tree, leading to ex...

The development of algorithms for semide nite programming is an active research area, based on extensions of interior point methods for linear programming. As semide nite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of infeasibility, nonzero optimal duality gaps, etc. Infeasible start algorithms have been proposed w...

We study interior-point methods for optimization problems in the case of infeasibility or unboundedness. While many such methods are designed to search for optimal solutions even when they do not exist, we show that they can be viewed as implicitly searching for well-defined optimal solutions to related problems whose optimal solutions give certificates of infeasibility for the original problem...

In this paper we present several \infeasible-start" path-following and potential-reduction primal-dual interior-point methods for nonlinear conic problems. These methods try to nd a recession direction of the feasible set of a self-dual homogeneous primal-dual problem. The methods under consideration generate an-solution for an-perturbation of an initial strictly (primal and dual) feasible prob...

In this paper we present several \infeasible-start" path-following and potential-reduction primal-dual interior-point methods for nonlinear conic problems. These methods try to nd a recession direction of the feasible set of a self-dual homogeneous primal-dual problem. The methods under consideration generate an-solution for an-perturbation of an initial strictly (primal and dual) feasible prob...

The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [...