# Optimization in MATLAB

## Description

Optimization is an interdisciplinary branch of mathematics that uses trends such as mathematical programming, statistics, and algorithm design to find the optimal point in optimization problems. Finding the optimal point has different meanings depending on the type of problem and is used in decision-making.

Optimization issues focus on maximization – such as profit, production line speed, more crop production, more bandwidth, etc. – or minimization – such as lower cost and risk reduction, etc., using one or more constraints. The basic idea of ​​optimization is to find the best answers to complex problems modelled in a mathematical language that improve or optimize the performance of a system.

Optimization is widely used in many disciplines today:

Structural engineering, road engineering, traffic, transportation, construction engineering, dam and network engineering, water resources systems, irrigation and drainage networks, water supply and sewerage networks, automotive engineering, aerospace, shipbuilding, military industries, distribution and consumption Energy optimization, design of industrial units, system engineering, various branches of electrical engineering and chemical engineering and materials engineering and operations research.

What topics are discussed in this educational video?

In this video tutorial, the main focus is on solving optimization problems with MATLAB software, and first, an introduction to the concepts is given, and then the various functions and features of MATLAB in optimization are fully explained with various examples.

The general form of an optimization problem

Linear constraint constraints

Inequality constraint

Boundaries and up and down variables are bounded constraints

How to write an objective function in MATLAB

How to write a multivariate function in MATLAB

Find the maximum of a function

Solve unconstrained problems

Problem-solving with nonlinear constraints

Outputs c and ceq

Set option

Show optimization problem-solving process

Bounding constraints

Unequal linear constraints

Matrix writing constraints

Set the initial guess

Set the maximum number of repetitions

Concept (TolX) Tolerance X

Concept of Tolerance Function (TolFun)

The process of solving an optimization problem

How much optimization settings to get a better answer?

Exit flag concept

Why has optimization stopped?

Which exit flag is correct?

Impact of TolX and TolFun on output

Linear programming

Linprog command

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