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Definition: Optimization

Optimization is a process concerned with the analysis and algorithmic aspects of either minimizing or maximizing an objective function, which is subject to certain constraints, such as non-negativity constraints, labour and raw material availability constraint, etc.

Engineering applications of this technique include portfolio optimization, optimal control, optimal design, machine learning, etc. Usually, optimization involves finding the “best possible” value of an objective function given a pre-defined domain.

Applications of optimization technique include the following:

1) Mechanics: Rigid body dynamics is one area where mathematical programming techniques are used very often as rigid body dynamics can be solved using ordinary differential equations. Aerospace engineering is also an area where it is frequently used.

2) Electrical Engineering: Common applications in electrical engineering include active filter design, space mapping design for microwave structures, electromagnetic design, etc.

3) Operations Research: Operations Research uses stochastic modelling and simulation for decision making in complex problems.

4) Economics: Microeconomics makes use of utility maximization problem (Consumer side) and its dual problem, the expenditure minimization problem (used by firms). Both of these are economic optimization problems. Market portfolio optimization is also an example of multi-objective optimization in economics.

5) Control Engineering: Modern controller designing uses mathematical optimization extensively.

6) Geophysics: Optimization is used in geophysical parameter estimation. Once a set geophysical measurements like seismic recordings are obtained, physical properties and other geometrical properties of underlying rock structures and fluids can be solved and obtained.

7) Petroleum Engineering: Optimization methods are used to construct computational models of oil reservoirs.


Hence, this concludes the definition of Optimization along with its overview.

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