## ME 575 Optimization Basics

## Main.OptimizationBasics History

Hide minor edits - Show changes to output

Deleted lines 64-82:

----

(:html:)

<div id="disqus_thread"></div>

<script type="text/javascript">

/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */

var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

/* * * DON'T EDIT BELOW THIS LINE * * */

(function() {

var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;

dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';

(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);

})();

</script>

<noscript>Please enable JavaScript to view the <a href="https://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>

<a href="https://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>

(:htmlend:)

Added lines 6-9:

(:html:)

<iframe width="560" height="315" src="https://www.youtube.com/embed/Q2dewZweAtU?list=PLLK3oSbvdxFdF67yVxF_1FQO9SbBY3yTL" frameborder="0" allowfullscreen></iframe>

(:htmlend:)

Changed line 51 from:

* What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

to:

* What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material? Please enter any that you'd like to share below in the comments section.

Changed line 37 from:

* Review information on optimization platforms ~~such as (2 or 3 is ~~fine):

to:

* Review information on optimization platforms (2 or 3 is fine) such as:

Changed line 7 from:

to:

* Complete the [[Main/InfoSheet | information sheet]] to tell me a little more about your background and interests

Changed lines 9-25 from:

to:

* Think of an optimization problem. Define the following for this optimization problem of your choice:

** Objective

** Analysis variables (Parameters)

** Design variables (Variables)

** Equality constraints

** Inequality constraints

** Continuous variables

** Discrete variables

* Optimizers sometimes report that the optimization problem is infeasible. What does infeasible mean and how can it generally be corrected?

* Give the general form of the following types of problems and list at least one method that is used to solve them.

** [[https://apmonitor.com/online/view_pass.php?f=lp.apm | Linear programming (LP)]]

** [[https://apmonitor.com/online/view_pass.php?f=qp2.apm | Quadratic programming (QP)]]

** [[https://apmonitor.com/online/view_pass.php?f=nlp.apm | Nonlinear programming (NLP)]]

** [[https://apmonitor.com/online/view_pass.php?f=milp.apm | Mixed integer linear programming (MILP)]]

** [[https://apmonitor.com/online/view_pass.php?f=minlp.apm | Mixed integer nonlinear programming (MINLP)]]

** Objective

** Analysis variables (Parameters)

** Design variables (Variables)

** Equality constraints

** Inequality constraints

** Continuous variables

** Discrete variables

* Optimizers sometimes report that the optimization problem is infeasible. What does infeasible mean and how can it generally be corrected?

* Give the general form of the following types of problems and list at least one method that is used to solve them.

** [[https://apmonitor.com/online/view_pass.php?f=lp.apm | Linear programming (LP)]]

** [[https://apmonitor.com/online/view_pass.php?f=qp2.apm | Quadratic programming (QP)]]

** [[https://apmonitor.com/online/view_pass.php?f=nlp.apm | Nonlinear programming (NLP)]]

** [[https://apmonitor.com/online/view_pass.php?f=milp.apm | Mixed integer linear programming (MILP)]]

** [[https://apmonitor.com/online/view_pass.php?f=minlp.apm | Mixed integer nonlinear programming (MINLP)]]

Changed lines 28-51 from:

to:

* Define the following and tell how it is relevant to optimization:

** Equation residuals

** [[https://en.wikipedia.org/wiki/Global_optimization | Global (vs. local) optimization techniques]]

** [[https://en.wikipedia.org/wiki/Lagrange_multiplier | Lagrange multiplier]]

** [[https://en.wikipedia.org/wiki/Jacobian_matrix | Jacobian matrix]]

** [[https://en.wikipedia.org/wiki/Hessian_matrix | Hessian matrix]]

** [[https://en.wikipedia.org/wiki/Sensitivity_analysis | Sensitivity analysis]]

** [[https://en.wikipedia.org/wiki/Robust_optimization | Optimization under uncertainty]]

* Review information on optimization platforms such as (2 or 3 is fine):

** [[https://www.aimms.com | AIMMS]]

** [[https://www.ampl.com | AMPL]]

** [[https://www.apmonitor.com | APMonitor]]

** [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

** [[https://www.gams.com | GAMS]]

** [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

** [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

** [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

** Additional tutorials available for the [[Main/TwoBarTruss | Two Bar Truss]] Problem

* What optimization software tutorials did you review?

* What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

** Equation residuals

** [[https://en.wikipedia.org/wiki/Global_optimization | Global (vs. local) optimization techniques]]

** [[https://en.wikipedia.org/wiki/Lagrange_multiplier | Lagrange multiplier]]

** [[https://en.wikipedia.org/wiki/Jacobian_matrix | Jacobian matrix]]

** [[https://en.wikipedia.org/wiki/Hessian_matrix | Hessian matrix]]

** [[https://en.wikipedia.org/wiki/Sensitivity_analysis | Sensitivity analysis]]

** [[https://en.wikipedia.org/wiki/Robust_optimization | Optimization under uncertainty]]

* Review information on optimization platforms such as (2 or 3 is fine):

** [[https://www.aimms.com | AIMMS]]

** [[https://www.ampl.com | AMPL]]

** [[https://www.apmonitor.com | APMonitor]]

** [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

** [[https://www.gams.com | GAMS]]

** [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

** [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

** [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

** Additional tutorials available for the [[Main/TwoBarTruss | Two Bar Truss]] Problem

* What optimization software tutorials did you review?

* What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

Changed lines 60-77 from:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

to:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

(:html:)

<div id="disqus_thread"></div>

<script type="text/javascript">

/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */

var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

/* * * DON'T EDIT BELOW THIS LINE * * */

(function() {

var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;

dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';

(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);

})();

</script>

<noscript>Please enable JavaScript to view the <a href="https://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>

<a href="https://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>

(:htmlend:)

(:html:)

<div id="disqus_thread"></div>

<script type="text/javascript">

/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */

var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

/* * * DON'T EDIT BELOW THIS LINE * * */

(function() {

var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;

dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';

(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);

})();

</script>

<noscript>Please enable JavaScript to view the <a href="https://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>

<a href="https://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>

(:htmlend:)

Changed line 37 from:

# Review information on optimization platforms such as:

to:

# Review information on optimization platforms such as (2 or 3 is fine):

Changed line 26 from:

->Example problems for each can be solved ~~at the following~~ links ~~by~~ selecting the run button (green arrow) ~~and viewing the results ~~in the window below.

to:

->Example problems for each can be solved by clicking on the links and selecting the run button (green arrow). The solution appears in the window below the model file by selecting the results table icon.

Changed line 26 from:

Example problems for each can be solved at the following links by selecting the run button (green arrow) and viewing the results in the window below.

to:

->Example problems for each can be solved at the following links by selecting the run button (green arrow) and viewing the results in the window below.

Added line 26:

Example problems for each can be solved at the following links by selecting the run button (green arrow) and viewing the results in the window below.

Changed lines 29-34 from:

## ~~Global (vs~~.~~ local) optimization techniques~~

## Lagrange multiplier

## Jacobian matrix

## ~~Hessian matrix~~

## Sensitivity analysis

## ~~Optimization under uncertainty~~

## Lagrange multiplier

## Jacobian matrix

## Sensitivity analysis

to:

## [[https://en.wikipedia.org/wiki/Global_optimization | Global (vs. local) optimization techniques]]

## [[https://en.wikipedia.org/wiki/Lagrange_multiplier | Lagrange multiplier]]

## [[https://en.wikipedia.org/wiki/Jacobian_matrix | Jacobian matrix]]

## [[https://en.wikipedia.org/wiki/Hessian_matrix | Hessian matrix]]

## [[https://en.wikipedia.org/wiki/Sensitivity_analysis | Sensitivity analysis]]

## [[https://en.wikipedia.org/wiki/Robust_optimization | Optimization under uncertainty]]

## [[https://en.wikipedia.org/wiki/Lagrange_multiplier | Lagrange multiplier]]

## [[https://en.wikipedia.org/wiki/Jacobian_matrix | Jacobian matrix]]

## [[https://en.wikipedia.org/wiki/Hessian_matrix | Hessian matrix]]

## [[https://en.wikipedia.org/wiki/Sensitivity_analysis | Sensitivity analysis]]

## [[https://en.wikipedia.org/wiki/Robust_optimization | Optimization under uncertainty]]

Changed lines 21-25 from:

## ~~Linear programming ~~(LP)

## ~~Quadratic programming ~~(QP)

## ~~Nonlinear programming ~~(NLP)

## ~~Mixed integer linear programming ~~(MILP)

## ~~Mixed integer nonlinear programming ~~(MINLP)

to:

## [[https://apmonitor.com/online/view_pass.php?f=lp.apm | Linear programming (LP)]]

## [[https://apmonitor.com/online/view_pass.php?f=qp2.apm | Quadratic programming (QP)]]

## [[https://apmonitor.com/online/view_pass.php?f=nlp.apm | Nonlinear programming (NLP)]]

## [[https://apmonitor.com/online/view_pass.php?f=milp.apm | Mixed integer linear programming (MILP)]]

## [[https://apmonitor.com/online/view_pass.php?f=minlp.apm | Mixed integer nonlinear programming (MINLP)]]

## [[https://apmonitor.com/online/view_pass.php?f=qp2.apm | Quadratic programming (QP)]]

## [[https://apmonitor.com/online/view_pass.php?f=nlp.apm | Nonlinear programming (NLP)]]

## [[https://apmonitor.com/online/view_pass.php?f=milp.apm | Mixed integer linear programming (MILP)]]

## [[https://apmonitor.com/online/view_pass.php?f=minlp.apm | Mixed integer nonlinear programming (MINLP)]]

Changed line 46 from:

## Additional ~~tutorial~~ available ~~under~~ the ~~next homework assignment for the [[Main/TwoBarTruss | Two Bar Truss]]~~

to:

## Additional tutorials available for the [[Main/TwoBarTruss | Two Bar Truss]] Problem

Added lines 45-46:

## Additional tutorial available under the next homework assignment for the [[Main/TwoBarTruss | Two Bar Truss]]

Changed lines 9-10 from:

# ~~Define the following for an optimization ~~problem ~~of your~~ choice:

to:

# Think of an optimization problem. Define the following for this optimization problem of your choice:

## Objective

## Objective

Changed line 7 from:

# Complete the [Main/InfoSheet | information sheet] to tell me a little more about your background and interests

to:

# Complete the [[Main/InfoSheet | information sheet]] to tell me a little more about your background and interests

Added lines 6-7:

# Complete the [Main/InfoSheet | information sheet] to tell me a little more about your background and interests

Changed line 35 from:

# Review ~~tutorials~~ on optimization platforms such as:

to:

# Review information on optimization platforms such as:

Deleted lines 43-44:

# How much time did you spend reviewing tutorials? _________ Hours

Changed lines 5-21 from:

!!!~~!~~ Optimization Basics

~~Review tutorials on optimization platforms such as:~~

* [[https:~~//www.aimms.com | AIMMS]]~~

* [[https://www.ampl.com | AMPL]]

* [[https://www.apmonitor.com | APMonitor]]

* [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

* [[https://www.gams.com | GAMS]]

* [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

* [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

Once you have done this, answer the following questions.

# Define the following types of parameters, variables, and equations

## Analysis variables

## Design variables

* [[https

* [[https://www.ampl.com | AMPL]]

* [[https://www.apmonitor.com | APMonitor]]

* [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

* [[https://www.gams.com | GAMS]]

* [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

* [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

Once you have done this, answer the following questions.

# Define the following types of parameters, variables, and equations

## Analysis variables

## Design variables

to:

!!! Optimization Basics

# Define the following for an optimization problem of your choice:

## Analysis variables (Parameters)

## Design variables (Variables)

# Define the following for an optimization problem of your choice:

## Analysis variables (Parameters)

## Design variables (Variables)

Added lines 33-42:

# Review tutorials on optimization platforms such as:

## [[https://www.aimms.com | AIMMS]]

## [[https://www.ampl.com | AMPL]]

## [[https://www.apmonitor.com | APMonitor]]

## [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

## [[https://www.gams.com | GAMS]]

## [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

## [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

## [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

## [[https://www.aimms.com | AIMMS]]

## [[https://www.ampl.com | AMPL]]

## [[https://www.apmonitor.com | APMonitor]]

## [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

## [[https://www.gams.com | GAMS]]

## [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

## [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

## [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

Changed line 56 from:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

to:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

Deleted lines 18-23:

# What optimization software tutorials did you review?

# What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

Added lines 44-49:

# How much time did you spend reviewing tutorials? _________ Hours

# What optimization software tutorials did you review?

# What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

Deleted lines 6-16:

Note: Each of the homework assignments are listed as either:

* Group Attach:group50.png

* Collaborative: Attach:collaborative50.png

* Individual: Attach:individual50.png

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

----

Changed lines 49-58 from:

## Optimization under ~~uncertainty~~

to:

## Optimization under uncertainty

----

Note: Each of the homework assignments are listed as either:

* Group Attach:group50.png

* Collaborative: Attach:collaborative50.png

* Individual: Attach:individual50.png

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

----

Note: Each of the homework assignments are listed as either:

* Group Attach:group50.png

* Collaborative: Attach:collaborative50.png

* Individual: Attach:individual50.png

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

Changed line 14 from:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. ~~Addition~~ guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

to:

Changed line 9 from:

Note: Each of the assignments are listed as either:

to:

Note: Each of the homework assignments are listed as either:

Changed lines 14-15 from:

This assignment can be completed as a collaborative ~~assignment~~.

to:

This assignment can be completed as a collaborative Attach:collaborative50.png assignment. Addition guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

Changed line 60 from:

## Optimization under uncertainty

to:

## Optimization under uncertainty

Added lines 4-14:

!!!! Optimization Basics

Note: Each of the assignments are listed as either:

* Group Attach:group50.png

* Collaborative: Attach:collaborative50.png

* Individual: Attach:individual50.png

This assignment can be completed as a collaborative assignment.

Attach:

Added line 14:

Changed lines 17-18 from:

(:htmlend:)

to:

# How much time did you spend reviewing tutorials? _________ Hours

# What optimization software tutorials did you review?

# What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

# Define the following types of parameters, variables, and equations

## Analysis variables

## Design variables

## Equality constraints

## Inequality constraints

## Continuous variables

## Discrete variables

# Optimizers sometimes report that the optimization problem is infeasible. What does infeasible mean and how can it generally be corrected?

# Give the general form of the following types of problems and list at least one method that is used to solve them.

## Linear programming (LP)

## Quadratic programming (QP)

## Nonlinear programming (NLP)

## Mixed integer linear programming (MILP)

## Mixed integer nonlinear programming (MINLP)

# Define the following and tell how it is relevant to optimization:

## Equation residuals

## Global (vs. local) optimization techniques

## Lagrange multiplier

## Jacobian matrix

## Hessian matrix

## Sensitivity analysis

## Optimization under uncertainty

# What optimization software tutorials did you review?

# What resources (at least 3) did you find particularly useful or informative as you reviewed the tutorials, documentation, videos, or other online material?

# Define the following types of parameters, variables, and equations

## Analysis variables

## Design variables

## Equality constraints

## Inequality constraints

## Continuous variables

## Discrete variables

# Optimizers sometimes report that the optimization problem is infeasible. What does infeasible mean and how can it generally be corrected?

# Give the general form of the following types of problems and list at least one method that is used to solve them.

## Linear programming (LP)

## Quadratic programming (QP)

## Nonlinear programming (NLP)

## Mixed integer linear programming (MILP)

## Mixed integer nonlinear programming (MINLP)

# Define the following and tell how it is relevant to optimization:

## Equation residuals

## Global (vs. local) optimization techniques

## Lagrange multiplier

## Jacobian matrix

## Hessian matrix

## Sensitivity analysis

## Optimization under uncertainty

Changed line 13 from:

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | ~~See ~~OptdesX ~~Section~~]]

to:

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | OptdesX - see OptdesX section]]

Added lines 1-19:

(:title ME 575 Optimization Basics:)

(:keywords nonlinear, optimization, engineering optimization, interior point, active set, differential, algebraic, modeling language, university course:)

(:description Introductory assignment on Optimization Techniques in Engineering at Brigham Young University:)

Review tutorials on optimization platforms such as:

* [[https://www.aimms.com | AIMMS]]

* [[https://www.ampl.com | AMPL]]

* [[https://www.apmonitor.com | APMonitor]]

* [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

* [[https://www.gams.com | GAMS]]

* [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | See OptdesX Section]]

* [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

Once you have done this, answer the following questions.

(:html:)

(:htmlend:)

(:keywords nonlinear, optimization, engineering optimization, interior point, active set, differential, algebraic, modeling language, university course:)

(:description Introductory assignment on Optimization Techniques in Engineering at Brigham Young University:)

Review tutorials on optimization platforms such as:

* [[https://www.aimms.com | AIMMS]]

* [[https://www.ampl.com | AMPL]]

* [[https://www.apmonitor.com | APMonitor]]

* [[https://www.solver.com/optimization-tutorial | Frontline Excel Solver]]

* [[https://www.gams.com | GAMS]]

* [[https://www.mathworks.com/products/optimization/ | MATLAB Optimization Toolbox]]

* [[https://apmonitor.com/me575/index.php/Main/OptimizationTools | See OptdesX Section]]

* [[https://software.sandia.gov/trac/coopr/wiki/Documentation/RelatedProjects | Python Optimization Packages]]

Once you have done this, answer the following questions.

(:html:)

(:htmlend:)