Problem 524. Sequential Unconstrained Minimization (SUMT) using Interior Penalty

Created by Robert Canfield

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function to find the values of a design variable vector,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x</w:t></w:r><w:r><w:t>, that minimizes a scalar objective function,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>f</w:t></w:r><w:r><w:t> (</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x</w:t></w:r><w:r><w:t> ), given a function handle to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>f</w:t></w:r><w:r><w:t>, and a starting guess,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x0</w:t></w:r><w:r><w:t>, subject to inequality constraints</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>g</w:t></w:r><w:r><w:t> (</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x</w:t></w:r><w:r><w:t> )&lt;=0 with function handle</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>g</w:t></w:r><w:r><w:t>. Use a logarithmic interior penalty for the sequential unconstrained minimization technique (SUMT) with an optional input vector of increasing penalty parameter values. That is, the penalty (barrier) function,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>P</w:t></w:r><w:r><w:t>, is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ P(x,r) = -sum(log(-g(x)))/r]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>r</w:t></w:r><w:r><w:t> is the penalty parameter.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

27 Solutions
7 Solvers

Last Solution submitted on May 15, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 19 Jun 2020

In this problem, we have the formula, or do we? There is more than one way to apply the interior penalty.

Solution Comments

Show comments

Problem Recent Solvers7

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 524. Sequential Unconstrained Minimization (SUMT) using Interior Penalty

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Problem 524. Sequential Unconstrained Minimization (SUMT) using Interior Penalty

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Players