Problem 485. Fletcher-Reeves Conjugate Gradient 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 an unconstrained 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>, 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 its gradient, 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>, a gradient tolerance,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>TolGrad</w:t></w:r><w:r><w:t>, and a maximum number of iterations,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>MaxIter</w:t></w:r><w:r><w:t>, using Fletcher-Reeves Conjugate Gradient Method.</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

164 Solutions
21 Solvers

Last Solution submitted on Mar 15, 2023

Last 200 Solutions

Solution Comments

Solution 62276

3 Comments

3 Comments

Alfonso Nieto-Castanon on 17 Mar 2012

something strange with test 2, my implementation fails on this test (because two iterations take me considerably closer to the minimum), perhaps this is something to do with the different forms of linesearch we are using?

Robert Canfield on 19 Mar 2012

Test case 2 is changed to account for your subsequent comment and to also to be far enough away from the solution so that it cannot converge in 2 iterations.

Rafael S.T. Vieira on 18 Jun 2020

Test case 2 still have problems, I have implemented the Fletcher-Reeves Conjugate Gradient Method from 1964, and it got rejected at the 2nd test. I believe the problem is that you are requesting precision from the approximation of an approximation. And this can only be done when we are very close to the solution. Test 1 seems to have the right precision for 1 iteration.

Problem Recent Solvers21

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 485. Fletcher-Reeves Conjugate Gradient Method

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers21

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Problem 485. Fletcher-Reeves Conjugate Gradient Method

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers21

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Players