The Objective Function quantifies the goal to be optimized (maximized or minimized). It maps decision variables to a real value representing cost, profit, distance, time, or other performance measure. In mathematical form: f(x) where x is the vector of decision variables. For linear programs: f(x) = cᵀx; for nonlinear: f(x) can be any differentiable or non-differentiable function. Multi-objective problems have vector-valued objectives f(x) = (f₁(x), f₂(x), ..., fₖ(x)). The objective function selection critically impacts solutions and requires careful modeling to capture true goals. Considerations include: units, scaling, linearization techniques, and handling multiple conflicting objectives through weighting or Pareto optimization.