LINEAR PROGRAMMING WITH INEQUALITY CONSTRAINTS VIA ENTROPIC PERTURBATION

A dual convex programming approach to solving linear programs with inequality con- straints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. An e- optimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Since cross-entropy minimization subject to linear inequality constraints is a special case of the perturbed linear program, the duality result becomes readily applicable. Many standard constrained optimization techniques can be specialized to solve the dual program. Such specializa- tions, made possible by the simplicity of the constraints, significantly reduce the computational effort usually incurred by these methods. Immediate applications of the theory developed include an entro- pic path-following approach to solving linear semi-infinite programs with an infinite number of ine- quality constraints and the widely used entropy optimization models with linear inequality and/or equality constraints.