presolver

A presolver is a component within a larger optimization solver, typically used in mathematical programming. Its primary function is to analyze and simplify a given optimization problem before the main solution algorithm is applied. The goal of presolving is to reduce the problem's size and complexity, thereby accelerating the overall solution process.

Common presolving techniques include identifying and removing redundant constraints, fixing the values of certain variables that can be determined statically, aggregating variables, and detecting infeasibility or unboundedness early on. For instance, a constraint that is always satisfied by the problem's domain can be safely removed. Similarly, if a variable must take a specific value due to its bounds and the constraints, its value can be fixed, and the problem reformulated with this fixed variable.

The effectiveness of a presolver can significantly impact the performance of an optimization solver. A good presolver can transform a difficult-to-solve problem into a much simpler one, making it tractable for standard algorithms. Conversely, an ineffective or overly aggressive presolver might inadvertently alter the problem or fail to find significant simplifications. Presolving is a crucial preprocessing step in many industrial-strength optimization solvers for linear programming, mixed-integer programming, and other related fields.