Lagrangianrelaxaatiota
Lagrangianrelaxaatiota, also known as Lagrangian relaxation, is a mathematical optimization technique used primarily in combinatorial optimization and operations research. The method transforms a complex, often intractable problem into a more manageable form by relaxing certain constraints, typically integer or binary constraints, into continuous ones. This relaxation allows the problem to be solved using standard optimization techniques, such as linear programming, while still providing useful insights into the original problem’s structure.
The approach is named after the Italian-French mathematician Joseph-Louis Lagrange, whose work on constrained optimization laid
Lagrangianrelaxaatiota is particularly useful in problems where the primal problem is difficult to solve directly, such
Despite its effectiveness, Lagrangian relaxation does not always guarantee an exact solution to the original problem.