Main

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Attach:group50.png This assignment can be completed in groups of two. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].
~~-> Attach~~:~~kkt_contour~~.~~png~~

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!!!! Part 3: 5 Minute KKT Exercise with both Inequality and Equality Constraints

This 5 minute exercise is similar to the previous ones but solves a problem with both equality and inequality constraints.

Download the following worksheet on KKT conditions with inequality and equality constraints. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example3.pdf|KKT Conditions Worksheet 3]]

* [[Attach:kkt_example3_solution.pdf|KKT Conditions Worksheet 3 Solution]]

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!!!! Part 4: 5 Minute Application Exercise for the Optimal Volume of a Tank

This 5 minute exercise covers an application to a tank volume optimization. In this case, we specify the final Lagrange multiplier of $8/ft'^3^'.

Download the following worksheet on this application of the KKT conditions. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example4.pdf|KKT Conditions Worksheet 4]]

* [[Attach:kkt_example4_solution.pdf|KKT Conditions Worksheet 4 Solution]]
~~* 2 Linear equality constraints~~

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!!!! Tutorial on the KKT Conditions

This 5 minute introductory video reviews the 4 KKT conditions and applies them to solve a simple quadratic programming (QP) problem with:

* 1 Quadratic objective function

* 3 Variables (x'_1_', x'_2_', x'_3_')

* 2 Linear equality constraints

Download the following worksheet on KKT conditions. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example1.pdf|Worksheet 1 on the KKT Conditions]]

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## Karush-Kuhn-Tucker (KKT) Conditions

## Main.KuhnTucker History

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!!!! Part 5: KKT Conditions for Dynamic Optimization

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!!!! Part 5: KKT Conditions for Dynamic Optimization

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Attach:group50.png This assignment can be completed in groups of two. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

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[[http://apmonitor.com/online/view_pass.php?f=qp3.apm | -> Attach:kkt_contour.png]]

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!!!! 5 Minute Tutorial on the KKT Conditions

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!!!! Part 1: 5 Minute Tutorial on the KKT Conditions

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!!!! 5 Minute Tutorial with KKT Conditions and Inequality Constraints

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!!!! Part 2: 5 Minute Tutorial with KKT Conditions and Inequality Constraints

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!!!! Part 3: 5 Minute KKT Exercise with both Inequality and Equality Constraints

This 5 minute exercise is similar to the previous ones but solves a problem with both equality and inequality constraints.

Download the following worksheet on KKT conditions with inequality and equality constraints. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example3.pdf|KKT Conditions Worksheet 3]]

* [[Attach:kkt_example3_solution.pdf|KKT Conditions Worksheet 3 Solution]]

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<iframe width="560" height="315" src="http://www.youtube.com/embed/JTTiELgMyuM?rel=0" frameborder="0" allowfullscreen></iframe>

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!!!! Part 4: 5 Minute Application Exercise for the Optimal Volume of a Tank

This 5 minute exercise covers an application to a tank volume optimization. In this case, we specify the final Lagrange multiplier of $8/ft'^3^'.

Download the following worksheet on this application of the KKT conditions. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example4.pdf|KKT Conditions Worksheet 4]]

* [[Attach:kkt_example4_solution.pdf|KKT Conditions Worksheet 4 Solution]]

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* [[Attach:kuhn_tucker_hw.pdf|Kuhn-Tucker and Lagrange Multiplier Homework]]

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* [[Attach:kuhn_tucker_hw.pdf|Karush-Kuhn-Tucker and Lagrange Multiplier Homework]]

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!!!! Tutorial on the KKT Conditions

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!!!! 5 Minute Tutorial on the KKT Conditions

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* 2 Linear equality constraints

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* [[Attach:kkt_example1.pdf|~~Worksheet 1 on the~~ KKT Conditions]]

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* [[Attach:kkt_example1.pdf|KKT Conditions Worksheet 1]]

* [[Attach:kkt_example1_solution.pdf|KKT Conditions Worksheet 1 Solution]]

* [[Attach:kkt_example1_solution.pdf|KKT Conditions Worksheet 1 Solution]]

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!!!! 5 Minute Tutorial with KKT Conditions and Inequality Constraints

This next 5 minute introductory is similar to the previous one but solves a problem with inequality constraints instead of equality constraints. The problem is a simple quadratic programming (QP) problem with:

* 1 Quadratic objective function

* 2 Linear inequality constraints

* 3 Variables (x'_1_', x'_2_', x'_3_')

Download the following worksheet on KKT conditions with inequality constraints. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example2.pdf|KKT Conditions Worksheet 2]]

* [[Attach:kkt_example2_solution.pdf|KKT Conditions Worksheet 2 Solution]]

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<iframe width="560" height="315" src="http://www.youtube.com/embed/JTTiELgMyuM?rel=0" frameborder="0" allowfullscreen></iframe>

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!!!! 5 Minute Tutorial with KKT Conditions and Inequality Constraints

This next 5 minute introductory is similar to the previous one but solves a problem with inequality constraints instead of equality constraints. The problem is a simple quadratic programming (QP) problem with:

* 1 Quadratic objective function

* 2 Linear inequality constraints

* 3 Variables (x'_1_', x'_2_', x'_3_')

Download the following worksheet on KKT conditions with inequality constraints. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example2.pdf|KKT Conditions Worksheet 2]]

* [[Attach:kkt_example2_solution.pdf|KKT Conditions Worksheet 2 Solution]]

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(:title Karush-Kuhn-Tucker (KKT) Conditions~~ and Lagrange Multipliers~~:)

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(:title Karush-Kuhn-Tucker (KKT) Conditions:)

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(:title Kuhn-Tucker Conditions and Lagrange Multipliers:)

(:keywords Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Kuhn-Tucker conditions and Lagrange multipliers including a number of problems.:)

!!!! Kuhn-Tucker Conditions

(:keywords Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Kuhn-Tucker conditions and Lagrange multipliers including a number of problems.:)

!!!! Kuhn-Tucker Conditions

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(:title Karush-Kuhn-Tucker (KKT) Conditions and Lagrange Multipliers:)

(:keywords Karush-Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Karush-Kuhn-Tucker (KKT) conditions and Lagrange multipliers including a number of problems.:)

!!!! Karush-Kuhn-Tucker (KKT) Conditions

(:keywords Karush-Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Karush-Kuhn-Tucker (KKT) conditions and Lagrange multipliers including a number of problems.:)

!!!! Karush-Kuhn-Tucker (KKT) Conditions

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!!!! Tutorial on the KKT Conditions

This 5 minute introductory video reviews the 4 KKT conditions and applies them to solve a simple quadratic programming (QP) problem with:

* 1 Quadratic objective function

* 3 Variables (x'_1_', x'_2_', x'_3_')

* 2 Linear equality constraints

Download the following worksheet on KKT conditions. The video below reviews the solution to this worksheet.

* [[Attach:kkt_example1.pdf|Worksheet 1 on the KKT Conditions]]

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<iframe width="560" height="315" src="http://www.youtube.com/embed/eaKPzb11qFw?rel=0" frameborder="0" allowfullscreen></iframe>

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(:title Kuhn-Tucker Conditions and Lagrange Multipliers:)

(:keywords Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Kuhn-Tucker conditions and Lagrange multipliers including a number of problems.:)

!!!! Kuhn-Tucker Conditions

The necessary conditions for a constrained local optimum are called the Kuhn-Tucker Conditions, and these conditions play a very important role in constrained optimization theory and algorithm development.

* [[Attach:kuhn_tucker_hw.pdf|Kuhn-Tucker and Lagrange Multiplier Homework]]

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(:keywords Kuhn-Tucker Conditions, Lagrange Multiplier, Optimization, Constrained:)

(:description Homework on Kuhn-Tucker conditions and Lagrange multipliers including a number of problems.:)

!!!! Kuhn-Tucker Conditions

The necessary conditions for a constrained local optimum are called the Kuhn-Tucker Conditions, and these conditions play a very important role in constrained optimization theory and algorithm development.

* [[Attach:kuhn_tucker_hw.pdf|Kuhn-Tucker and Lagrange Multiplier Homework]]

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