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How to code this quadratic minimization problem subject to a linear constraint?

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Armando MAROZZI
Armando MAROZZI on 22 Mar 2020
Edited: Armando MAROZZI on 22 Mar 2020
After having performed Factor Analysis (FA), I am now trying to implement the following rotation strategy (Swanson 2017 - details of rotation strategy in appenix A) to interpret the three factors structurally and economically. The strategy is in 3 steps but I will report just the first one as the other steps will follow suit:
1) Quadratic minimization problem subject to a linear constraint:
s.t.
where
is the 80x3 matrix of unrotated factors, (3x1) is the first column of λ which is the 7x3 matrix of factor loadings and is the third column of U which is a 3x3 orthogonal matrix. and are known (find data attached: fa_pre = (80x3) and lambda_1 = (1x3)). Obviously, I would like to solve it for to fully have .
Can you help me code the first minimization problem?

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