The Pros And Cons Of Optimization

Optimization is a scientific approach to solve for the best solution for a problem. Its applications emerge in many different areas is real-life. For instance, you need to minimize the labor cost in a business or to maximize the profit of a product. On the other hand, in an airline company, you need to minimize the flight time of a plane or the fuel cost. In basic words, in an optimization issue, you need to either minimize or maximize the result (the objective or cost function). Of course, you can't generally optimize a situation without some particular constraints. For example, how does a worldwide petroleum refiner choose where to purchase raw petroleum, where it should be processed, what product should be produced by using it, where to

For instance, the decision variables can be the quantities of the assets to be allocated, the quantity of units to be produced, or even both. The decision maker looks for the value set of these obscure variables that will give an optimal solution for the problem. The decision variables are normally indicated by x1 , x2 ,... or else x, y, and z. But, model developers are allowed to define the names of variables. Even though, some software products set limits on the length of variable names, others permit any length of alphabetic or alphanumeric characters. At ties, it is useful to characterize meaningful names for variables. Shorter names are usually used since, by using shorter names it decreases the probability of making errors in typing and writing, and also it makes the model to look more

A Globally Optimal Solution is the probably best solution which meets all Constraints.

The Simplex LP Solver regularly finds the Globally Optimal Solution at the point where 2 or more Constraints intersect.

3.2. NONLINEAR PROGRAMMING (NLP)
A model in which the objective function and the greater part of the constraints (except for integer constraints) are smooth nonlinear functions of the decision variables is known as a nonlinear programming (NLP) or a nonlinear optimization problem. Such problems are inherently harder to understand than linear programming (LP) problems. They may be convex or non-convex, and a NLP Solver should determine or approximate derivatives of the problem functions numerous times throughout the course of the optimization. Since a non-convex NLP may have numerous feasible regions and different locally optimal points inside such regions, there is no basic or quick approach to determine with sureness that the problem is infeasible, that the objective function is unbounded, or that an optimal solution is the "global optimum" over all feasible