# Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

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## MATLAB Example: Solve Constrained Nonlinear Optimization, Problem-Based

Intermediate
Example
Theory

This example shows how to find the minimum of a nonlinear objective function with a nonlinear constraint by using the problem-based approach.

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## Converting Constrained Optimization to Unconstrained Optimization Using the ...

54 min
Beginner
Video
Theory

In this video we show how to convert a constrained optimization problem into an approximately equivalent unconstrained optimization problem using the penalty...

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## Solving Systems of Equations Using the Optimization Penalty Method

44 min
Beginner
Video
Theory

In this video we show how to solve a system of equations using numerical optimization instead of analytically solving. We show that this can be applied to e...

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## Using ‘fminsearch’ to Minimize a Function Specified by a File with Extra Par...

25 min
Beginner
Video
Application

In this video we show 4 different ways to use/call Matlab’s ‘fminsearch’ function to perform unconstrained optimization.Topics and timestamps:0:00 – Introduc...

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