definition v4 of optimization

Optimization is a human-made formal method of selecting values for a set of decision variables so as to maximize or minimize a specified objective function over a feasible region. Parameters: (1) the decision space — the variables and their domains; (2) the objective function — the scalar quantity to be extremized; (3) the constraint set — equalities and inequalities restricting feasible solutions (unconstrained optimization is the special case where the feasible region is the whole space); (4) the solution procedure — an algorithm or calculus method (gradient descent, Newton's method, linear programming) that navigates the decision space toward an optimum. It persists through mathematical notation and theorems (convexity, KKT conditions, duality), computational implementations in numerical libraries, and institutionalized practice across operations research, engineering, economics, and machine learning. Without the formal pairing of objective function and constraint structure, optimization degenerates into preference or trial-and-error, losing the guarantees (existence, optimality, convergence) that define it. [formal: optimization | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]