Problem 527. Augmented Lagrange Multiplier (ALM) Method

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 and equality constraints with function handles</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>&lt;=0 and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>h</w:t></w:r><w:r><w:t>=0, respectively. Use the Augmented Lagrangian Multiplier Method (a.k.a., the Method of Multipliers) and return the estimate of Lagrange multipliers</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>u</w:t></w:r><w:r><w:t> for inequalities, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v</w:t></w:r><w:r><w:t> for equality constraints.</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

57 Solutions
6 Solvers

Last Solution submitted on Jan 16, 2021

Last 200 Solutions

Problem Recent Solvers6

Problem Tags

aoe4084 constrained minimization

Community Treasure Hunt

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

Start Hunting!

Problem 527. Augmented Lagrange Multiplier (ALM) Method

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Problem 527. Augmented Lagrange Multiplier (ALM) Method

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Players