Optimization problem

An optimization problem seeks a minimum or maximum of an objective function over choices allowed by specified constraints.

Objective function: A function assigning a numerical value to each candidate choice in a problem. Its values express what the optimization problem seeks to minimize or maximize.
Linear programming: Optimization of a linear objective over a region defined by linear constraints. It is a tractable, widely used subclass with a distinctive geometric solution structure.
Convex optimization: Optimization in which the feasible set is convex and the objective has compatible convexity or concavity. Its structure makes local optima global under standard formulations.
Operations research: The discipline of using mathematical models and analytical methods to support decisions in complex systems. It applies optimization to planning, allocation, scheduling, and logistics.
Feasible region: The set of candidate points satisfying all constraints in an optimization problem. Only points in this region can qualify as solutions.
Gradient descent: An iterative method that updates variables in the direction opposite the objective's gradient. It searches for local minima when the objective is differentiable.
Nonlinear programming: Optimization problems with nonlinear objective functions or constraints. Nonlinearity can create multiple local optima and complicate global solution.
Economic optimization: The use of optimization models to represent choices by consumers, firms, or policymakers under scarcity. Economic models express trade-offs as objectives constrained by resources and rules.
Constraint (mathematics): A condition restricting the values that variables in a mathematical problem may take. Constraints carve the feasible region from all possible choices.
Simplex algorithm: A method for solving linear programs by moving between vertices of their feasible polyhedra. It exploits the fact that a linear program has an optimal vertex when a finite optimum exists.

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