Uncontrained optimisation.

Thread starter kk88sg
Start date Oct 31, 2007
Tags

Optimisation

In summary, unconstrained optimization is a type of mathematical optimization where the objective function and constraints do not depend on each other. It involves finding the optimal value of a variable without any restrictions on its values. Examples include finding maximum or minimum values of a function, optimizing machine learning models, and fitting data points. It differs from constrained optimization where the objective function is subject to constraints. Common methods used in unconstrained optimization include gradient descent, Newton's method, and the Nelder-Mead algorithm. Unconstrained optimization has various applications in science, including physics, engineering, economics, and machine learning, to find optimal solutions in a wide range of problems.

Oct 31, 2007

kk88sg

Find the critical point(s) for the function:
f(x,y)=5x^2-3xy+y^2-15x-y+2 and classify it.

Can anyone help? Thanks.

Physics news on Phys.org

Oct 31, 2007

EnumaElish

Science Advisor

Homework Helper

So you have any thoughts or views about the problem and how it could be approached?

1. What is unconstrained optimization?

Unconstrained optimization is a mathematical optimization problem where the objective function and the constraints do not depend on each other. This means that the goal is to find the optimal value of a variable without any restrictions on its values.

2. What are some examples of unconstrained optimization?

Examples of unconstrained optimization include finding the maximum or minimum value of a function, finding the best fit line for a set of data points, and optimizing the parameters of a machine learning model.

3. How is unconstrained optimization different from constrained optimization?

In constrained optimization, the objective function is subject to one or more constraints. This means that the optimal value of the variable must satisfy these constraints. In unconstrained optimization, there are no such restrictions on the variable.

4. What are some common methods used in unconstrained optimization?

Some common methods used in unconstrained optimization include gradient descent, Newton's method, and the Nelder-Mead algorithm. These methods rely on iteratively updating the value of the variable in order to find the optimal solution.

5. What are the applications of unconstrained optimization in science?

Unconstrained optimization has numerous applications in science, including in physics, engineering, economics, and machine learning. It is used to find optimal solutions in a wide range of problems such as maximizing profit, minimizing energy consumption, and predicting the behavior of complex systems.