With ongoing advances in hardware and software, the bottleneck in linear programming is no longer a model solution, it is the correct formulation of large models in the first place. During initial formulation (or modification), a very large model may prove infeasible, but it is often difficult to determine how to correct it. We present a formulation aid which analyzes infeasible LPs and identifies minimal sets of inconsistent constraints from among the perhaps very large set of constraints defining the problem. This information helps to focus the search for a diagnosis of the problem, speeding the repair of the model. We present a series of filtering routines and a final integrated algorithm which guarantees the identification of at least one minimal set of inconsistent constraints. This guarantee is a significant advantage over previous methods. The algorithms are simple, relatively efficient, and easily incorporated into standard LP solvers. Preliminary computational results are reported. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

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G iven an infeasible set of linear constraints, finding the maximum cardinality feasible subsystem is known as the maximum feasible subsystem problem. This problem is known to be NP-hard, but has many practical applications. This paper presents improved heuristics for solving the maximum feasible subsystem problem that are significantly faster than the original, but still highly accurate.

T his paper develops a method for moving quickly and cheaply from an arbitrary initial point at an extreme distance from the feasible region to a point that is relatively near the feasible region of a nonlinearly constrained model. The method is a variant of a projection algorithm that is shown to be robust, even in the presence of nonconvex constraints and infeasibility. Empirical results are presented.

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