Heuristic based on Elastic programming (Chinneck 2001).

Dynamic IIS generation

Partial IIS (Irreducible Infeasible Subsystem) covering formulation with dynamic IIS generation (Parker
& Ryan 96)

LP with equilibrium constraints

Formulations as LP with equilibrium constraints and concave
minimization on polyhedra tackled by successive linearizations
(Mangasarian et al. 94/96, Bennett et al. 97)

First branch-and-cut algorithm (Pfetsch 02/05) based on
polyhedral study in Amaldi et al. 03.

The Feasopt feature in Ilog Cplex: an infeasibility analysis tool that "...accepts an infeasible model and
selectively relaxes the bounds and constraints, minimizing a [user defined] weighted penalty function."

Relaxation method

It is a simple algorithmic framework for solving systems of linear inequalities, see e.g. [11,22]. At every iteration the attention is focused on
reducing the violation of a single inequality. Given a feasible system
with
and
, as well as
a starting point
,
such a method generates a
sequence
of approximate
solutions. [more...]
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