What is optimization for data science?

Overview

Data science is a field used to analyze the vast volume of data through different techniques to make it understandable. To understand data science, we need to have a good understanding of these three concepts: statistics, linear algebra, and optimization.

Optimization

Optimization is a procedure or technique which is used to find the most efficient resolution. Its value may be minimum or maximum, which depends upon the requirement. For example, if a firm is required to find a way to earn a maximum profit on their products, then the condition will be maximum, and if they want to find a way through which their firm gets minimum product cost on production, then the requirement will be minimum.

Usage of optimization

Optimization works as a backbone for almost all techniques used in data science. It also helps the business leaders to predict their business plans, and it allows the government to find an appropriate resolution for human welfare by analyzing data they provide suitably optimization helps in numerous other sectors like economic, artificial intelligence, and many more.

So, let’s understand what the optimization problem is and its types.

Elements of the optimization problem are:

1. The objective function
2. Decision variables
3. Constraints

The objective function is the first element of an optimization problem if the function f(y) is used to find the minimize or maximize value. As a general rule, we talk about minimization issues, this is essential since, in case you have a boost issue with f(y) , we can change it over to a minimization issue with - f(y). Thus, without loss of consensus, we can check.

Decision variable is the second element. The decision variable can observe the ideal variable to solve the optimization problem. Which can only be done by decision variable. F(y)=3x+2 in this y is a decision variable. There are three types of variables: continuous, integer, and mixed.

Continuous variable should be ongoing, assuming if the y variable can take a limitless number of values. For this situation, y can handle an unlimited number of values between -3 to 5.

$-f(y)$$,$$y$ $∈$ $(-3,5)$

Integer variable can be any number that might be positive or negative, or even 0.

$-f(y)$,$y$ $∈$ {0,3,4,5,7)

Mixed variable is a set of variables that contains both continuous and integer variables.

$-f(y)$,$y1$ $∈$ $(-3,5)$

and

$-f(y)$,$y2$ $∈$ {0,3,4,5,7)

Constraints are used to restrict the options for decision variables in an optimization problem, e.g., you have $30 in your pocket, and you want to buy b burgers which one may cost you almost $6/per burger, and you want to buy some h hot dogs which cost you $1.

$6b$ $+$ $1h$ $≤$ $30$

In this problem, 30 is the limit that plays the role of constraint. 6b and 1h showing the prices of products.

There are two types of constraints:

• Linear constraints limit the decision variable to a linear class.

• Non-linear constraints limit the decision variable to a non-linear class.

So, for solving any optimization problem, we need to look for its elements.

Types of optimization

Linear programming: If the optimization element decision variable remains continuous and both of the remaining elements become linear, it will become a linear programming problem.

Non-linear programming: If the optimization element decision variable remains continuous and either one of the remaining elements becomes non-linear, it will become a non-linear programming problem.

Linear integer programming: If the object function and constraints are linear and the decision variable y is an integer, then it will be called a linear integer programming problem.

Non-linear programming: If the object function and constraints are non-linear and the decision variable is an integer, then it will be called a non-linear integer programming problem.

Binary integer programming: If the objective function and constraints are linear and decision variable y can only have binary integer ${0.1}$ options, then it will be called a binary integer programming problem.

Mixed-integer linear programming: If the objective function f and the constraints are both linear, and decision variable y is a mixed variable that can be continuous or integer, it will be called a mixed-integer programming problem.

Mixed-integer non-linear programming: If one of the objective function f or the constraints are non-linear, and the decision variable y is a mixed variable that can be continuous or integer, it will be called a mixed-integer non-linear programming problem.