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There are many example online of how to use Lagrange multipliers to solve Markowitz's minimum variance problem (namely find the weightings for the portfolio which minimises variance for a given return with constraints on the calculated return of said portfolio and the sum of weighting of all assets within the portfolio to 1). However I can't find an example of how to go the other way, find the weighting of the portfolio which maximises return for a given variance. I know they'd both fall on the efficient frontier..

Can anyone help?

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