Convex Programming: What is it?

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Convex programming, a subclass of nonlinear programming, is a type of programming that generalizes and unifies other types, including linear programming, least squares, and quadratic programming. The concept of convex programming offers support for a large number of theoretical and practical applications. It boasts efficient algorithms which make it beneficial for a programmer to use and develop this type of programming. Convex programming requires extensive experience and expertise on the part of the programmer, as well as a disciplined learning process. While not a new concept, it is still used in many disciplines and applications that require complex and technical mathematics.

Three principles are important for the application of convex programming: optimization, numerical computation, and convex analysis. Increased computing power and breakthroughs in complex algorithms allowed scientists and mathematicians to develop this type of programming and use it for problem solving. Convex programming has provided its users with useful computational tools that help solve higher class problems in the areas of linear programming and least squares. Engineers have found this type of programming useful for functions such as signal processing, control, circuit design, networking, communication, etc.

Using convex programming requires an understanding of linear algebra, optimization, and vector calculus. Convex sets are quite common and used in this type of programming. Programmers use these convex sets to solve some vector optimization problems. Another element common to this type of programming is a convex function.

Applications of convex programming are common in the field of microeconomics, especially in the determination of maximized profit and maximized consumer preference. This is a form of optimization and requires the complex math found in convex programming. A common problem that is considered and solved in this discipline is what is called a mathematical optimization problem. This problem uses a vector to represent and abstract the optimal choice from a certain set of choices.

Another example of this type of abstract problem occurring in a different discipline includes portfolio optimization, where one looks for the best capital investment option from a given set of assets. In computers and electronic design, device sizing is another optimization problem, where the best length and width for a device, such as a circuit board, must be determined. Data fitting, another aspect of computers and electronic devices, seeks to find the model from a pool of potential candidate models that best fits one type of previously observed data or previously acquired information.

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