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How does nonlinear programming differ from linear programming?
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optimization
Constraint set bounded by the five lines x1 = 0, x2 = 0, x1 = 8, x2 = 5, and x1 + x2 = 10. These enclose an infinite number of points that represent feasible solutions.
Nonlinear programming differs from linear programming primarily in the mathematical nature of the objective function and constraints. In linear programming, problems are solved using linear functions where variables are subject to linear constraints. Conversely, an optimization problem is classified as nonlinear if the objective function or any of the constraints are nonlinear functions of the variable vector.12
Key distinctions include:
- Modeling Capability: Nonlinear programming is required when a system's essential features—such as exponential chemical reactions, risk variance in finance, or physical distances in molecular structures—cannot be accurately expressed through linear functions.23
- Computational Complexity: Linear programming problems are generally considered computationally "cheap" to evaluate. In contrast, nonlinear problems can be computationally expensive and often involve complex, iterative algorithms that generate a sequence of guesses to identify an optimal value.2
- Optimality: While linear programming often identifies a clear optimal solution, nonlinear programming algorithms may struggle to find a global optimum, frequently requiring the user to settle for a local optimum—the best value within a specific region of feasible solutions.2
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