Skip to main content
11 events
when toggle format what by license comment
Jun 18, 2021 at 17:51 vote accept RSMax
Jun 11, 2020 at 23:19 history edited Robert Israel CC BY-SA 4.0
added 810 characters in body
Jun 11, 2020 at 20:51 history edited Robert Israel CC BY-SA 4.0
added 933 characters in body
Jun 11, 2020 at 19:49 comment added Robert Israel Linear programming in Excel. But the algorithm I presented in the EDIT is simpler (though maybe not so easy to program in Excel). Maybe I should make it more explicit.
Jun 11, 2020 at 17:14 comment added RSMax If by linear programming you mean something else than Newton's method, I am very much interested. As I need to ultimately code the result, anything easier and/or more efficient than Newton's method will be received with open arms. Would you mind elaborating a bit? Thank you sir.
Jun 11, 2020 at 17:08 comment added RSMax Whether I minimize the trace or the sum the squares of all elements on the diagonal, my current issue (under the Newton's method approach) is that my "main" unknown is a matrix ($\boldsymbol{P}$, whereas the Lagrange multipliers are scalars, and I'm confused about how to wrap those 3 under a common structure so that I can recursively update it and converge toward a solution. Should I add rows and columns to the unknown $\boldsymbol{P}$ matrix so that it incorporates $\lambda_1$ and $\lambda_2$ on the main diagonal?
Jun 11, 2020 at 17:03 comment added RSMax I totally agree with the EDIT section, this is something I have observed in practice using Excel's solver. What remains encouraging is that through this scheme, $P_{11}$ will nonetheless be less than $\pi_1$, given that $\pi_1 \geq 0.5$, ergo the diagonal has still been minimized in some way.
Jun 11, 2020 at 17:03 history edited Robert Israel CC BY-SA 4.0
deleted 2 characters in body
Jun 11, 2020 at 15:50 history edited Robert Israel CC BY-SA 4.0
added 1036 characters in body
Jun 11, 2020 at 15:04 comment added RobPratt Alternatively, an objective to minimize $\sum_i P_{i,i}^2$ yields a (convex) quadratic programming problem.
Jun 11, 2020 at 14:41 history answered Robert Israel CC BY-SA 4.0