Optimization, defined.

A mathematical optimization method for finding the best outcome in a model with linear relationships between variables, subject to linear constraints.

An optimization method where some or all variables must take integer values, used for problems involving yes/no decisions, scheduling, and routing.

A paradigm for solving combinatorial problems by defining variables, their domains, and constraints that must be satisfied simultaneously.

The problem of finding optimal routes for a fleet of vehicles to serve a set of customers, minimizing total distance or cost while respecting constraints.

A class of computational problems for which no known algorithm can find optimal solutions in polynomial time. As problem size grows, solve time grows exponentially.

Finding the best solution from a finite but exponentially large set of possibilities, where the solution is a combination of discrete choices.

An algorithm for solving integer and combinatorial optimization problems by systematically exploring the solution space while pruning branches that cannot contain optimal solutions.

An algorithm for solving linear programming problems by moving along the edges of the feasible region to find the optimal vertex.

The discipline of applying analytical methods to help make better decisions, using mathematical modeling, optimization, simulation, and statistical analysis.

An optimization method where the objective function is quadratic and the constraints are linear, commonly used in portfolio optimization and control systems.