Recently, the Area of Mixed Integer Nonlinear Programming(Minlp) Has Experienced Tremendous Growth and a Flourish of Research Activity.In This Article We Will Give a Brief Overview of Past Developments In the Minlparena and Discuss some of the Future Work That Can Foster the Development Ofminlp In General And, In Particular, Robust Solver Technology For the Practicalsolution of Problems. Mixed-Integer Programs (Mip's) Involving Logicalimplications Modeled Through Big-M Coefficients, Are Notoriously Among Thehardest to Solve. In This Paper We Propose and Analyze Computationally Anautomatic Problem Reformulation of Quite General Applicability, Aimed Atremoving the Model Dependency on the Big-M Coefficients. Our Solution Schemedefines a Master Integer Linearproblem (Ilp) With No Continuous Variables, Which Contains Combinatorialinformation on the Feasible Integer Variable Combinations That Can Be\Distilled" from the Original Mip Model. the Master Solutions Are Sent Toa Slave Linear Program (Lp), Which Validates Them and Possibly Returnscombinatorial Inequalities to Be Added to the Current Master Ilp. Theinequalities Are Associated to Minimal (Or Irreducible) Infeasible Subsystemsof a Certain Linear System, and Can Be Separated Efficiently In Case the Mastersolution Is Integer. the Overall Solution Mechanism Resembles Closely Thebenders' One, But the Cuts We Produce Are Purely Combinatorial and Do Notdepend on the Big-M Values Used In the Mip Formulation. This Produces an Lprelax ...