NONLINEAR PROGRAMMING Meaning and
Definition
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Nonlinear programming refers to a subfield of mathematical optimization that deals with solving optimization problems where the objective function or the constraints, or both, involve nonlinear relationships or functions. It is concerned with finding the optimal solution for these types of problems, which may involve minimizing or maximizing an objective function while considering a set of constraints.
In nonlinear programming, the objective function is not a linear function, meaning it cannot be represented as a simple sum of variables multiplied by constants. Instead, it may involve complex mathematical relationships, such as polynomials, exponentials, or trigonometric functions. Similarly, the constraints in nonlinear programming are also nonlinear expressions that restrict the feasible region for the variables.
The main challenge in nonlinear programming is that these problems do not have straightforward analytical solutions like linear programming problems. Therefore, various algorithms and techniques are employed to approximate the optimal solution. These methods include gradient-based approaches like Newton's method and quasi-Newton methods, as well as heuristic methods like genetic algorithms and simulated annealing.
Nonlinear programming finds wide applications in various fields, including engineering, economics, finance, physics, and operations research. It enables the optimization of complex systems and processes by considering the effects of nonlinear relationships and constraints. By finding the optimal solution, nonlinear programming helps in making informed decisions, improving resource allocation, and enhancing the overall efficiency and performance of systems.
Etymology of NONLINEAR PROGRAMMING
The word "nonlinear programming" can be broken down into two components: "nonlinear" and "programming".
- The term "nonlinear" comes from mathematics and refers to a relationship or function that is not described by a linear equation. In the context of optimization problems, "nonlinear" implies that the objective function or constraints involved are not linear.
- The term "programming" originates from the field of operations research and has a slightly different meaning than its standard usage. In this context, "programming" refers to the process of finding an optimal solution to a problem, specifically through the selection or allocation of resources.
When combined, "nonlinear programming" refers to the area of optimization that deals with problems where the mathematical relationships involved are nonlinear and require specific algorithms and techniques to find optimal solutions.
